"I wanted to" vs "I want to" when referring to the future

Both can be used. The verb tense is tied to Tony's desire, not to the future event.

For example:

Tony wanted me to go out with him tomorrow night [but he changed his mind and doesn't want me to anymore].

Tony wants me to go out with him tomorrow night [and I'm looking forward to it].

Also, wanted is fine, even if the desire is still there:

Tony wanted me to go out with him tomorrow night [and he still does].

Note, too, that emphasis can play a role:

Tony wanted me to go out with him tomorrow night [and not you].

If the tense actually were tied to the temporal nature of the event, then the only possible construction we could use would be:

Tony will want me to go out with him tomorrow night.

But that's certainly not required.

As to why people choose one verb form over the other (when both can be used), it can just be a matter of personal preference.

But outside of any context, I would say that you wouldn't normally just use the past tense. If somebody came up to me and said, "Somebody wanted to ask you out tomorrow," I would look at them blankly for a second and then say, "And . . . ?"