The wiring is a mess
Here's what you can do.
In the sub-panel, take the small 12 guage red, and move it from wherever it's attached (can't tell because the pic didn't quite show) and attach it to T4 on the interlock relay (where the large 10 guage red wire is attached, both red wires will now be on T4)
Now, disconnect the 12 guage blue wire from wherever it's attached (can't tell because the pic didn't quite show) and attach it to T3 on the interlock relay (Where the 10 guage black wire is attached, both the 10 guage black and the 12 guage blue will be on T3)
The black wire on T1 will probably be a lonely soldier, just cap and tape it so it won't brush anything.
Then, turn on the power, and go to the main terminal block on the spa control box. Your readings should be as follows:
terminals 1 and 3 -->240v
terminals 2 and 4 -->240v
any terminal (1-4) and 5 --->120V
Terminal 5 and ground ---> 0v
If this is what you get, turn it on and enjoy!
One more note:
The neutral is pigtailed to the ground in the subpanel. If you can figure out which wire is supposed to be neutral and which is ground (why oh why did someone run a black as either a Neutral or Ground!!) you can put the neutral wire on the neutral bar in the subpanel, and remove the black jumper that connects Neutral and Ground. Not the end of the world, and it will probably work fine the way it is, but it's so easy to fix, I would.