I use both the “get paid early” feature and the budgeting features in Monzo. If I accept my salary early the day before I am officially paid, the “you finished the month with x” figure in the spending report is incorrect, as it includes the salary payment.
Eg, on Thursday, I start with a balance of £100, get paid early and end the day with £200. My pay period officially ends on the Friday, so when I get my spending report on the Saturday, it tells me I ended the period with £200.
What should happen, is that when I accept the salary early, the budgeting period ends, and my spending report tells me I ended the period with £100. Any spending on Thursday night after getting paid comes out of the new budget that started at 16:00 (or whenever I manually accepted the payment).