I recently had a contactor put on and now it is coming on when my thermostat is set on off. What might be the problem?

Does the fan inside also come on or just the ac unit?

Yes the fan comes on too.

Sounds like a t-stat problem then. Is it a programmable stat? Digital stat? Or old murcury?

It is a digital stat

Will it also go off by its self? Or once it comes on, it stays on? When it comes on does it say cooling is on?

It goes off by itself and the thermostat is still saying off/