If my refund is set to be sent on a certain day should I expect it 2 days earlier since that's what this service advertises?

Once the IRS releases your funds, how soon they deposit to your account depends on your banking institution. The date on the IRS website is typically the date the IRS will send it to your bank, however it could take a day or more to see the funds in your bank.

Here is an FAQ from the IRS:

What is happening when Where’s My Refund? shows my refund’s status as approved?

We’ve approved your refund. We are preparing to send your refund to your bank or directly to you in the mail. This status will tell you when we will send the refund to your bank (if you selected the direct deposit option). Please wait 5 days after we’ve sent the refund to check with your bank about your refund since banks vary in how and when they credit funds. (It could take several weeks before you receive a mailed refund check.)

 https://www.irs.gov/refunds/tax-season-refund-frequently-asked-questions