Only the Present Exists

Bill offers a definition of presentism:

PP:  Only the present present exists: there are (tenselessly) many times, and every time t is such that everything that exists exists (tenselessly) at t.

I'm not sure I understand this.  Especially the underlined phrase.  Bill goes on to say,

(PP) strikes me as problematic. (PP) implies that there are (tenselessly) many different times. But there cannot be (tenselessly) many times if at each time there is only what exists at that time. For if at each time there is only what exists at that time, then at each time there are no times other than that time.  Is there a formulation of presentism that is consistent with its own truth?  I suspect that there isn't.

The conclusion 'at each time there are no times other than that time' seems intuitively right.  Time has time for at most one time at a time, as it were.  But how does this rule out there being (tenselessly) many times?  I don't think it does.  We can rephrase Bill's sentence as

At each time, if there is only what exists at that time, then there are no times other than that time.

It's clear that the 'at each time' tenses the conditional.  It locates it at a particular time.  But the sentence itself is a universal generalisation over all times, and hence tenseless.  Bill seems to want to speak of times as existents within time, just like spatio-temporal particulars and events.  That's a category mistake, surely?

Returning to Bill's definition (PP), I struggle with the phrase 'exists (tenselessly) at t'.  The 'tenselessly' and the 'at t' together are oxymoronic.