Let me explain it all in detail.
The Slavic languages originally had 4 past tenses, of which two were simple and two analytical.
The simple past tenses of the Old Church Slavonic verb “to see” видѣти (perfective aspect), оувидѣти (imperfective aspect) are:
Aorist: видѣхъ “I saw (once)”
Imperfect: видѣахъ “I saw (usually, several times)”
Analytical past tenses:
Perfect: ѥсмь оувидѣлъ “I have seen (masculine)”
Pluperfect: бѣахъ видѣлъ “I had seen (masculine)”
And there were 2 Future tenses:
Future I: начьнѫ/хоштѭ/имамь видѣти “I will see”
Future II: бѫдѫ видѣлъ “I will have seen (masculine)”
There used to be 2 active past participles, видѣв(ши) and видѣлъ “that saw”, of which the former could be used attributively, but the latter was used exclusively in analytical tenses, in Perfect, Pluperfect, Future II, and also in the Subjunctive Mood, видѣлъ бимь “I would see (masculine)”.
During the last millennium, most Slavic languages lost the simple past tenses, they remained only in Bulgarian and in a somehow changed form in Macedonian. The rest of the Slavic languages (like Russian, Ukrainian, and Polish) have kept just the Perfect tense (and Pluperfect, too, in some languages like Ukrainian). In the East Slavic languages the auxiliary verb ‘to be’ in the present tense mostly fell out of usage, that is why in Russian the modern “past tense” form of the verb does not have any person as a verb form should do, but instead it has number and gender forms like adjectives and participles, since a participle it actually is. The Polish language has kept the auxiliary ‘to be’, but as a clitic, not as a stand-alone form: pisałam “I wrote (feminine)” has this clitic -m at the end which is all that has remained of the original ѥсмь (jesmĭ) “[I] am”. A very similar situation is in the West Ukrainian dialects, where the support of the neighboring Polish and Slovak languages helped to keep those Perfect personal clitics: писала-м “I wrote (feminine)”.
As for the Future tenses, in most modern Slavic languages they got contaminated, the two future tenses fused into one tense: the Future II auxiliary verb ‘to be’ in its Future form (‘to be’ is the only Slavic verb that has a future tense stem) began to be used with the infinitive, like in Future I. Still, Polish has kept the Future II as it used to be, but only formally, of its ‘Future Perfect’ meaning only ‘Future’ remains, the ‘Perfect’ component of the meaning got lost, so now Polish has two analytical future forms, Future I of ‘to be’ + Infinitive and Future II of ‘to be’ + the exclusive special participle in
-ł. ‘I will write’ in the two Polish analytical Future tenses:
Future I: będę pisać
Future II: będę pisał
These two Future tenses have absolutely the same meaning, the difference being only stylistic. As far as I know, the modern Polish Future II is considered to be somehow more bookish and polite, although some use the two tenses indiscriminately or prefer just one of them. It is hard to tell for sure how a similar future tense appeared in the West Ukrainian dialects, it is either by parallel evolution or by Polish influence, or maybe both.
As you can see, those examples you presented have nothing to do with past, except that the participle used in those analytical future forms is also used to form past tenses. If in English in Past Perfect ‘I had seen’ and Future Perfect ‘I'll have seen’ there's the same form ‘seen’, it doesn't mean there's something past in the English future, it is the ‘Perfect’ thing that is common there.