My lease states rent is due by the 25th of each month or a $10 per day late fee would inccur. I'm paid until the 1st of the month so how can they charge a late fee? Is it legal?

The lease states it is due on the 25th so it is due on the 25th.

Did you just move in or is this a recurring issue?

Call or go to your leasing or landlords office and bring a copy of your lease with you. Sometimes this can be an error in the management companies billing system. The billing cycle may be set up just as you said, the 25th. It bills you as a new entry and may not be taking in account that your rent is paid up until the 1st. And may be flagging you as late. If the property manager is not thorough, they may just be responding to a prompt by their software. If the person or company is doing their accounting by hand, could be human error.

If you have just moved in, there may be a prorating confusion.

The lease is the lease and if you signed it and it was executed properly between you and the landlord and the lease is in compliance with your states laws, you can pretty much expect it's terms and verbiage are enforcable. So, whatever the payment terms are, that is what you should expect to follow.

... I'm paid until the 1st of the month so how can they charge a late fee? ...

Look at it this way: you pay the rent for any given month (until the 1st of the following month), on or before the 25th of that month. So rent for February was due by January 25th, and when it is paid you are current for the entire month of February. You are current until March 1.