I am very familiar with posting direct deposits as i have done this in previous work. First of all when your employer says they "send" your check to the bank of Tuesday, what they are really doing is keying it into the computer. When your employer does this, the reason they "send" it on Tuesday is because its just like a check card purchase in that it takes 2 business days to post. It is a "transaction". Your payroll HAS to know this because you said you get paid on Thursdays. Your employer fully expects you to not get your pay even ONE day early. You are suppose to get paid on Thursday and you do. Your funds are posted and available to you Thursday morning.
Second, , , if you are getting overdraft fees, , i can assure you it is not on anything you initiate on Thursday morning. More likely, its items done prior to Thursday morning, meaning you spent more money than you had prior to Thursday. Go ask your bank to show you actual posting order not just your history transaction list and you'll see.
You cannot go Wed. night to Wal-mart and use your check card, thinking "Oh I get paid in the morning". It use to be credits would always post before debits, , but we are in the 21st century now. Banks know what time you use your card and what time your deposit comes in . And contrary to popular believe, , when you use your check card, it does not immediately "post" to your acct. The merchant only puts a temporary hold on those funds. The hold is released after the first processing night. Meaning that if your trying to use the ATM instead of your check register to keep up with your balance, , your probably goin to have Overdrafts.
Most people who complain about overdrafts, probably 90%, either (a) don't know what a check register is. ( b) have one but do not write everything down, and do not keep a running balance. or (c) Round up and think thats gonna keep them okay.
By the way, , , all banks post at night, , , they all only do it once.
Praise be to the person that pioneers the posting system to be "real time"