Your correct sentences are those that use the subjunctive:
- No se supone que te rías.
No deberías reírte. (Your behavior is inappropriate)
- No se supone que estés aquí.
No deberías estar aquí. (You're not invited.)
With "deber", the subjunctive is also necessary, but for me, it changes the meaning* of the sentence:
- No se supone que debas reírte.
No necesitas reírte. (It was a bad joke.)
- No se supone que debas estar aquí.
No necesitas estar aquí. (Go home, it's not compulsory to be here.)
* [Someone has just told me they don't completely agree with the change of meaning, so I'll let other users debate my perception if necessary.]
As for the verb "ir", there is also a change of meaning for me --something will happen, even if we know it's not going to cause the expected effect:
- No se supone que te vayas a reír. (I'd be surprised if you laughed.)
- No se supone que vayas a estar aquí. (We know you won't be here, unless you condescend.)
If you find "no se supone que" with the imperfect or the conditional, then it's a question. (It's a particular use of past tenses as a prospective):
- ¿No se supone que te ibas a reír? (You were supposed to laugh, why aren't you?)
- ¿No se supone que estarías aquí? (Weren't you supposed to be here?)
- ¿No se supone que estabas enfermo? (Weren't you supposed to be sick?)