First and foremost, Altaic is a controversial grouping of languages at best. So take claims about them with a grain of salt, though it may be useful to view them as a language area. But it still doesn't clear up what we're talking about. So-called "Micro-Altaic" (Turkic, Mongolic, and Tungusic languages)? Or "Macro-Altaic" (Micro-Altaic plus Korean and Japanese)?
Turkish (a Turkic language) and Mangghuer (a Mongolic language) both have indefinite articles, but they look nothing like one another. The Turkish indefinite article is bir, while the Mangghuer indefinite article is ge. The origin of the Turkic form is fairly clear: it's just the number one, a meaning it retains in modern Turkish. The origin of the Mangghuer is debated, but is likely also from 'one', which is Mangghuer nige (Slater 2003: 312). Not even people who claim Altaic is a valid grouping claim Turkic bir and Mongolic nige are related words, so the innovation must have come after the languages split up, if they even were a singular grouping.
These articles do indeed function like other indefinite articles. There are some fine grained differences, but that's to be expected across languages. A lot of work has been done on what is called differential object marking (DOM) in Turkish, where an object can optionally take the accusative case marker -i for a specific meaning when compared to an object that does not take the accusative case marker. Compare the following:
- Ali bir kitabı aldı. 'Ali bought a certain book.'
- Ali bir kitab aldı. 'Ali bought a book.' (examples from Enç 1991)
So there are tons of similarities (English and Turkish indefinite articles both from a word originally meaning 'one'), but differences (Germanic languages except some varieties of Afrikaans don't have DOM but do have articles, Turkish has DOM which interacts with its articles, Japanese has DOM but does not have articles).