I changed the dates from 25jun to 26jun to perform the tests and my results do not match your example.
You could comment.
<table style="font-family:Arial; font-size:12pt; border-style: groove ;border-color:#0000FF;background-color:#fffcf9; color:#000000; "><tr><td ><b>Sheet2</b></td></tr></table>
<table border="1" cellspacing="0" style="font-family:Calibri,Arial; font-size:11pt; background-color:#ffffff; "> <colgroup><col style="font-weight:bold; width:30px; " /><col style="width:76.04px;" /><col style="width:140.67px;" /><col style="width:126.42px;" /><col style="width:95.05px;" /><col style="width:111.21px;" /></colgroup><tr style="background-color:#cacaca; text-align:center; font-weight:bold; font-size:8pt; "><td > </td><td >A</td><td >B</td><td >C</td><td >D</td><td >E</td></tr><tr style="height:19px ;" ><td style="font-size:8pt; background-color:#cacaca; text-align:center; " >1</td><td style="background-color:#92d050; font-weight:bold; text-align:center; ">Name</td><td style="background-color:#92d050; font-weight:bold; text-align:center; ">Received date</td><td style="background-color:#92d050; font-weight:bold; text-align:center; ">Email Sent 1</td><td style="background-color:#92d050; font-weight:bold; text-align:center; ">Email Sent 2</td><td style="background-color:#92d050; font-weight:bold; text-align:center; ">Email Sent 3</td></tr><tr style="height:19px ;" ><td style="font-size:8pt; background-color:#cacaca; text-align:center; " >2</td><td >Peter_KU</td><td style="text-align:right; ">26/06/2019</td><td style="text-align:right; ">24/06/2019</td><td style="background-color:#ffff00; text-align:right; ">26/06/2019</td><td style="text-align:right; ">23/06/2019</td></tr><tr style="height:19px ;" ><td style="font-size:8pt; background-color:#cacaca; text-align:center; " >3</td><td >James_BR</td><td > </td><td style="text-align:right; ">23/05/2019</td><td style="text-align:right; ">23/05/2019</td><td style="text-align:right; ">23/05/2019</td></tr><tr style="height:19px ;" ><td style="font-size:8pt; background-color:#cacaca; text-align:center; " >4</td><td >John_BL</td><td style="text-align:right; ">23/05/2019</td><td > </td><td style="text-align:right; ">23/05/2019</td><td style="text-align:right; ">23/05/2019</td></tr><tr style="height:19px ;" ><td style="font-size:8pt; background-color:#cacaca; text-align:center; " >5</td><td >Peter_KU</td><td style="text-align:right; ">26/06/2019</td><td style="background-color:#ffff00; text-align:right; ">26/06/2019</td><td style="background-color:#ffff00; text-align:right; ">26/06/2019</td><td style="background-color:#ffff00; text-align:right; ">26/06/2019</td></tr><tr style="height:19px ;" ><td style="font-size:8pt; background-color:#cacaca; text-align:center; " >6</td><td >James_BR</td><td style="text-align:right; ">23/05/2019</td><td style="text-align:right; ">23/05/2019</td><td > </td><td style="text-align:right; ">23/05/2019</td></tr><tr style="height:19px ;" ><td style="font-size:8pt; background-color:#cacaca; text-align:center; " >7</td><td >John_BL</td><td style="text-align:right; ">26/06/2019</td><td style="background-color:#b2a1c7; text-align:right; ">26/06/2019</td><td style="background-color:#b2a1c7; text-align:right; ">26/06/2019</td><td style="background-color:#b2a1c7; text-align:right; ">26/06/2019</td></tr><tr style="height:19px ;" ><td style="font-size:8pt; background-color:#cacaca; text-align:center; " >8</td><td >Peter_KU</td><td style="text-align:right; ">23/05/2019</td><td style="text-align:right; ">23/05/2019</td><td style="text-align:right; ">23/05/2019</td><td > </td></tr><tr style="height:19px ;" ><td style="font-size:8pt; background-color:#cacaca; text-align:center; " >9</td><td >James_BR</td><td style="text-align:right; ">26/06/2019</td><td style="background-color:#b8cce4; text-align:right; ">26/06/2019</td><td style="background-color:#b8cce4; text-align:right; ">26/06/2019</td><td style="background-color:#b8cce4; text-align:right; ">26/06/2019</td></tr><tr style="height:19px ;" ><td style="font-size:8pt; background-color:#cacaca; text-align:center; " >10</td><td >John_BL</td><td style="text-align:right; ">22/05/2019</td><td style="text-align:right; ">22/05/2019</td><td style="text-align:right; ">22/05/2019</td><td style="text-align:right; ">22/05/2019</td></tr></table>
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<table style="font-family:Arial; font-size:12pt; border-style: groove ;border-color:#0000FF;background-color:#fffcf9; color:#000000; "><tr><td ><b>Sheet1</b></td></tr></table>
<table border="1" cellspacing="0" style="font-family:Calibri,Arial; font-size:11pt; background-color:#ffffff; "> <colgroup><col style="font-weight:bold; width:30px; " /><col style="width:76.04px;" /><col style="width:144.48px;" /><col style="width:128.32px;" /></colgroup><tr style="background-color:#cacaca; text-align:center; font-weight:bold; font-size:8pt; "><td > </td><td >A</td><td >B</td><td >C</td></tr><tr style="height:19px ;" ><td style="font-size:8pt; background-color:#cacaca; text-align:center; " >1</td><td >Name</td><td >Received date count</td><td >Emails sent 1;2;3</td></tr><tr style="height:19px ;" ><td style="font-size:8pt; background-color:#cacaca; text-align:center; " >2</td><td >Peter_KU</td><td style="text-align:right; ">2</td><td style="text-align:right; ">4</td></tr><tr style="height:19px ;" ><td style="font-size:8pt; background-color:#cacaca; text-align:center; " >3</td><td >James_BR</td><td style="text-align:right; ">1</td><td style="text-align:right; ">3</td></tr><tr style="height:19px ;" ><td style="font-size:8pt; background-color:#cacaca; text-align:center; " >4</td><td >John_BL</td><td style="text-align:right; ">1</td><td style="text-align:right; ">3</td></tr></table><br /><table style="font-family:Arial; font-size:10pt; border-style: groove ;border-color:#00ff00;background-color:#fffcf9; color:#000000; "><tr><td ><b></b></td></tr><tr><td ><table border = "1" cellspacing="0" cellpadding="2" style="font-family:Arial; font-size:9pt;"><tr style="background-color:#cacaca; font-size:10pt;"><td >Cell</td><td >Formula</td></tr><tr><td >B2</td><td >=COUNTIFS(Sheet2!$B$2:$B$10,TODAY(),Sheet2!$A$2:$A$10,A2)</td></tr><tr><td >C2</td><td >=SUMPRODUCT((Sheet2!$C$2:$E$10=TODAY())*(Sheet2!$A$2:$A$10=A2))</td></tr></table></td></tr></table>