This is a case where a simple common sense approach to teaching English is at odds with the formal definitions of some linguists.
To those who define tense as a modification of a verb to indicate time, English has two tenses, "past" and "non-past".
However, English tends to be analytic, and where other languages use a tense (changing the form of the verb) English uses syntax. It is quite reasonable to talk about the "will future tense", the "going to future", the "present continuous", the "present perfect" and so on.
The combination of words "will + verb" functions very much like the combination of morphemes "verb root + future suffix" in languages like French. It is unnecessarily pedantic and potentially confusing to insist that this isn't a "tense" for anyone who is learning English.
Of particular note in the question is the assertion that in the phrase "will jump", the verb "jump" is in present tense. It isn't, it is a bare infinitive and doesn't have any tense. This is most clearly seen in the second example where "be" is never present tense.
While I said that English has two tenses, this definition of tense is not universal, and some include all modification of the verb phrase to indicate time as a tense, and not just modifiction of the verb. In this definition of tense, modifying a verb by using a modal like "will" is tense.
So be not afraid of calling "will jump" the future tense of the verb "jump".