I agree with the rest here - getting it square now is imperative.
I'd start by setting up the table saw with a cut-off fence - i.e. a short fence clamped to the main fence and adjust distance from far side of the blade to the short fence to the tenon length and the blade height to trim the tenon shoulders even and square. A lot of the strength of the M & T joint comes from the shoulders sitting firmly and squarely. Then trim the tenons as needed (with a wide chisel or shoulder plane). If one side or both are loose, you can glue pieces of veneer to the tenon faces to tighten the joint. Since the veneer will not show, the variety used does not matter. After gluing on the veneer, you can gently trim the tenon to adjust the fit.
I'd also chamfer all ends of the tenon to avoid having the end-grain catch on the edge of the mortice and tearing away when fitting the pieces.
One other thing to check. If the small adjustments made to square the tenon shoulders shortens the remaining leg length, then corresponding adjustment will need to be made at the top of all other legs to ensure the top has a square base to sit on. Your picture does not show any joinery at the top, but if you plan to cut tenons to go into the table, adjust the length to be the same and then use the same set-up from above get square shouldered tenons at the top as well. From the picture it appears you will not be cutting much off the legs and should not shorten the legs much more the a sixteenth of an inch. After cutting the shoulders with the table saw, I'd use a bandsaw to cut the tenon cheeks. Cut the tenons very slightly over size and trim with a chisel of shoulder plane to get a tight fit in the top mortises. If these tenons will show through the top, don't chamfer them. You may want to slightly angle the ends of the mortice and cut slots in the tenon to allow a wedge to be driven into the visible end of the tenon to secure the joint.
You might also consider draw boring for pegs at the bottom - i.e. drill a hole in the face of the piece and mark the tenon where the hole meets the tenon, then drill the same size hole in the tenon, offset by about 1/8 of the pin size towards the tenon cheek. The pins used must be very straight grained to avoid having them break when driven in. The idea of the small offset is to have the pin pull the joint together very tightly - hence part of the need for square faces.
Hope this helps answer your question.
If not I will try to clarify further.