Hei Apoorva,
You are correct in that future tense ("futuuri") as such doesn't exist. (
https://fi.wikipedia.org/wiki/Futuuri#Futuuri_suomen_kieless%C3%A4 ), so it's replaced by other means of describing the future.
There are pretty good examples in the site that you linked from, and you are typically fine if you pick one of those versions. I suggest you read them and try to practice how to use them.
Now, the format of Tulen/tulemme etc. has its uses, but it's a bit less common and somewhat formal.
I think the best equivalent of this is the "shall"-format in English:
"Tulette lukemaan minusta lehdistä" = "You (all) shall read about me in newspapers"
"Tulemme laulamaan virren 516" = "We shall be singing the hymn (number) 516"
"Tulet saamaan kielteisen päätöksen" = "You shall be receiving a negative resolution."