What ultimatum? An ultimatum is saying 'if you dont do X by Y time, Z will happen".

You dont do that, you express what you want and that's it. She either complies or she doesn't. Either way you know what to do.

What dread do you wanna apply? This may sound brutal but you're not capable to apply dread if your girl is chatting with random dudes, not yet. Whats your other option? Increase your SMV which could take a long time just so MAYBE you can apply dread then?

I may be reading you the wrong way but from the sound of it:

1) She has the power in the relantionship

2) You are afraid to lose her

3) You are being jealous but are afraid that jealousy will make you lose her

4) You will most likely tell her, then she will argue, and you will let it slide

5) You tell her to stop, she complies, but will keep talking to the dude behind your back

To be honest, there's no win for you here with this girl. Fully expect the relationship to be over within 2 months. Dont see it as a negative thing, but be prepared anyway and have a contingency plan.