The dictionary definition of a STALKER is " a person who harasses or persecutes (ill treat) someone with unwanted and obsessive attention", so has Dev done this, yes he has been a bit obsessive but can that categorise him as a stalker as Sonakshi said, I would say no. He never did it with the intention of harassing or hurting Sonakshi. So calling him a stalker in my opinion is a bit of over-reaction.
Now coming to whether he is being POSSESSIVE, I would say he is on the cusp of doing that. Right now he is being OVER PROTECTIVE. In fact a lot of times these two terms are interchangeable. So yes he is being possessive only with the intention to protect her. Also I believe in any relationship especially that of a husband-wife's a bit of possessiveness is not wrong as it gives the other person a sense of how much his/her partner values his/her position in their life.
Saying this I can try to make sense of the reactions of both Dev & Sonakshi. While Dev has seen right in his childhood what the loss of a dear one (his father) meant along with how her mother used to carry a knife for protection, to add to that he is still guilty of not being there for Sonakshi when she needed him the most during her pregnancy & then the bus incident. All this adds to his current reaction, unless he himself or someone makes him come out of this, he is going to be the same.
As for Sonakshi the last seven years has made her strong & independent. And probably for the first time in seven years she is feeling that she is getting dependent on someone and probably that gives her a sense of weakness. If we remember just after her confession she expressed this fear to her parents that whether she did right thing as she feared she might make herself weak again. So seeing Dev's reaction now she might be thinking that. But I would definitely want her to understand Dev a bit more the way she understands others.
At the end of this all I would want is for both to sit together and sort this out before things go out of hand.
Apologies for the long post, this is just my POV, no offence.
PS - On a lighter note I guess Dev's hairstyle & the background music somehow adds to the feeling that Dev is getting possessive or rather stalking 😆