The language's most basic verb marking is for aspect: -ile marks perfective (which may of course overlap with past tense meanings). If not perfective then the default verb ending in -a occurs, which is prototypically present.
There is also an anterior (hence "tense") marker kade (which no one noticed before, but which I believe to be grammaticalized for the most proficient speakers who use the pidgin regularly).
Thus kade idli-ile [ANT eat-PFV] 'had eaten' = PLUPERFECT.
Kade idla 'was eating' (PROG) or 'used to eat' (HAB.PST) does not have a perfective meaning.
The language marks future (which I've always thought of as tense, since there are no other modal verbs or auxiliaries; but I'm not averse to considering zo as a modal.) Hence zo idala 'will eat' (FUT); zo idl-ile (FUT + PRF) 'will have eaten' = rare but attested.
So I now think the best analysis is that the language has (FUT) + ANT + PFV as its basic template.
All three can be combined - however they are not adjacent -but I've not come across an idiomatic example. My informant thinks that zo kade idlile 'will have had eaten' is okay given a particular context (and preceding irrealis temporal clause).