-ing clauses (like infinitive clauses) have no tense. They can be attached to a main clause in any tense, and normally indicate that the action happens at the same time as the main action:
He went out, carrying his briefcase.
He will go out, carrying his briefcase.
He was about to go out, carrying his briefcase.
(We can specify the action at a different time by using constructions like after xxx-ing or before xxx-ing, or by having xxx-ed; but if we don't do that, the clause happens at the same timeas the matrix verb).
The complication here is that the verb in the -ing clause is "wish", which can take a finite (tensed) clause as its complement. In this case, the embedded clause is backshifted if necessary according to the matrix verb, but is interpreted relative to when the wishing happens.
He sits by the phone wishing it would ring.
is present, referring to a hoped-for future event. (It could be wishing it will ring, but would seems more idiomatic to me. If the verb were hoping, then hoping it will ring is natural )
He sat/was sitting by the phone wishing/hoping it would ring.
is past, referring to an event which was future relative to when he was sitting. In the case of hoping, the will gets back-shifted to would because the matrix verb is past: this doesn't affect wishing, which already prefers would.
He will be sitting by the phone wishing it would ring/hoping it will ring.
is future, referring to an later event.
But if the embedded clause has a past tense (for a counterfactual wish)
He sits/was sitting/will sit by the phone wishing it had rung.
refers to his wishing for an event in the past relative to when he is wishing - whenever that may be specified as. This is necessarily a counterfactual.