Those are all correct and are examples of two different tenses (you have two examples of perfect present and one of progressive). There is also a third tense; simple. Your examples actually have three different verbs and you could rephrase your statement in any of those three tenses with each of those three verbs for several combinations, all of which are correct.
Consider the following:
Present perfect tense:
Joe has started to follow Mike.
Joe has followed Mike.
Joe has begun following Mike.
Sentences in present perfect tense actually look like they use a past tense verb (started, followed, begun), but it is preceded by the present tense of the verb to have to affect the entire sentence.
Joe is following Mike.
Joe is starting to follow Mike.
Joe is beginning following Mike.
There is also simple tense; Joe followed Mike. Joe started to follow Mike. Joe began following Mike.