Whether compound past tenses such as passé composé are formed with être or avoir is a purely grammatical rule. It has no impact on the meaning, and in particular no impact on the “kind of pastness”. A passé composé with être is no more (or less) of a present perfect than a passé composé with avoir.
It's true that when the past tense is formed with être, the sentence is grammatically ambiguous: “je suis [participe passé]” could be a passé composé in the active voice, a present in the passive voice, or the present tense of être with an adjective that is an attribut du sujet¹. The choice of verb and the meaning determine which interpretations are possible.
Only certain kinds of verbs can have their compound past tenses formed with être: mostly state changes, for which “I have [changed to] state” and “I am [in this] state” are often equivalent. The default interpretation (inasmuch as there is one) varies from verb to verb. For example, “il est mort” (“he has died” or “he is dead”) implies that the person is still dead, because dying is normally irreversible, so the default interpretation is that it indicates the current state (être + attribut du sujet). At the other end of the spectrum, “il est parti” (“he is gone”) does not indicate where the person is now, because “parti” is not really used as an adjective, so it's clearly a passé composé. In between, something like “il est sorti” (“he has gone out” or “he is out”) is ambiguous, and only the context can tell whether this means that the person is currently out.
Context does make the grammatical interpretation change, and this is completely transparent for a native speaker. “Il est mort hier” (“he died yesterday”) is perfectly fine, and a native speaker would not consider this weird in any way. Similarly,“il est sorti, il reviendra demain” (“he's gone out, he'll be back tomorrow”) and “il est sorti fumer deux fois” (“he went out twice to smoke”) are both perfectly fine.
You can find examples of synonymous verbs, one of which takes the auxiliary être and the other avoir. For example, in many contexts, arrêter (to stop) can be indifferently reflexive or intransitive in common usage. These two sentences have exactly the same meaning.
Son cœur s'est arrêté de battre.
Son cœur a arrêté de battre.
¹ Verbs that take the auxiliary être are normally intransitive and therefore don't have a passive voice. However, dual-usage verbs do exist, where the verb can either be transitive and use avoir or intransitive and take être. For example, “elle est montée” is usually a past tense (“elle est montée sur la colline”: “she climbed up the hill”), but it could be a passive voice (“la pièce est montée par un metteur en scène inconnu”: “the play is produced by an unknown director”) or an adjective (“l'affaire est montée de toutes pièces”: “the whole business was entirely made up”).