In English, your consecutio temporum is usually called the ‘sequence of tenses’. There is a general rule that in the principal sentence (i) a primary tense is followed in the subordinate clause by a primary tense, and (ii) a historic tense by a historic tense. In subordinate clauses the subjunctive is usual, incomplete action being represented by the ...
This is what Adolf V. Streng (Latinan kielioppi, 5th edition, 1936) says in §161.2:
Finnish: Toisen tahi kolmannen asteen konjunktiivinen sivulause mukautuu predikaattinsa tempuksen puolesta sitä lähinnä hallitsevan sivulauseen mukaan.
Free translation: A conjunctive subordinate clause of second or third order adapts to the closest governing clause ...
If we have a subordinate clause depending on superordinate conjunctive clause, we must consider the tense of the conjunctive:
(A) present or perfect "logic" (assimilable to a present), it should be used the tenses prescripted by the consecutio temporum of the primary times, like in Sen. ep. 32,1:
sic vive tamquam quid facias auditurus sim
Tuomo Pekkanen's Ars Grammatica – Latinan kielioppi (§116, lisäys 3) mentions that the historical present can be treated as either a present tense or as a past tense when consecutio temporum is concerned.
It gives this example without any citation or further explanation:
Quod cum videret, quaerit, quae causa sit/esset.
When he saw it, he ...
When a clause is subordinate to a nominal form of a verb (anything that does not have a grammatical person), the conjunctive predicate of the subordinate clause follows the predicate verb of its main clause, not the nominal form.
For example: Me adiit mirans, cur Graeci sic loquerent. (Here loqui follows adire, not mirari.)
There is, however, an exception:
The are two clauses here:
"He refused to fight"
"until reinforcements came"
Clause 1 is the governing clause, 2 the subordinate one.
When translating to Latin, you first translate the governing clause.
Depending on the type of refusal, you could pick perfect (he stated once that he will not fight) or imperfect (he consistently refused all requests before ...