Is the following sentence correct?
He is just buying a gift for his mother.
I am not sure if it is all right to have that "just" there and this lead me to believe that maybe the tense is wrong.
There is absolutely nothing "incorrect" about your sentence. Whether it is appropriate to use just, right now, or at the moment in that sentence depends on the context/style. If you are saying "He is just buying a gift for his mother" to someone in speech, then the sentence is fine, as noted by StoneyB.
Dad: Where is your brother? What's taking him so long?
Daughter: Relax dad! He will be out in a minute. He is just buying a gift for mom.