If someone is a person who pays great attention to detail and who does things precisely, can we call him an “attentive person”? I think we can call someone, “meticulous” to mean that. I am not sure about using “attentive” to mean that because I think “attentive” is specifically used if someone listens to or watches something carefully like in, “He is an attentive student” meaning he is a student who watches and listens to the class carefully, or like in “This is a very attentive audience”. Do you think we can say like, “John is an attentive person” if he is generally careful of what he does?
The primary meaning of 'attentive' is 'listening or watching carefully'. It can also mean someone who attends to matters, perhaps in response to a need. It doesn't really mean attention to detail in an active way.
For someone who actively, rather than passively, notices and responds to details, even minor ones, we would normally either say they were 'meticulous' as you suggested, or say that they have "attention to detail". Other commonly used synonyms include 'thorough' and 'conscientious'.
In the context of someone who is considerate or courteous with other people, especially when attentive to detail, if you come from Spanish (and perhaps other Romance languages?), perhaps you got some influence from the Spanish "atento/a" (c.f. DRAE definition 2, in Spanish).
Anyway, this is similar to this definition of "attentive":
1.1 Assiduously attending to the comfort or wishes of others; very polite or courteous.
‘the hotel has a pleasant atmosphere and attentive service’