if I understand correctly 3 months is the time you all have been together? if so thats a very short amount of time INTPs can last YEARS and YEARS and still not know if they want that relationship, think of this....INTP lives in a fictional world of what is possible.........You dont. You as an INFJ u live in a world of Knowing what is gonna happen that is your Ni. ....INTPs will stick around someone friend or otherwise just to see how it all plays out. they are observers, but they never really DO anything .....or so they think....INTP is fully oblivious as to how their actions influence others, they have "perfect deniability" and OH dont you DARE try to hold them accountable for anything.... LOL.
In any case your INTPs behavior with the phone is actually VERY INTP. INTps like facebook and other social media, it allows them to portray an :image: of themselves, one which they have control over and they like that!! INTPs are freaking weird, awkward, mentally skewed, narcissistic, beings. they know this and the world knows this, THUS social media allows them to seem like normal functional humans and they love this! .....it also gives them the chance to make their lazy boring lives to look like they have meaning and that they are doing something.....aka TRAVEL......they totally suck at maintaining relationships, friends family love, etc. because it all requires A. Too much work and B. for them to actually acknowledge and meet the needs of another human........"a toddler does not meet the needs of the parent" this is the best quote for us to understand with INTPs and make no mistake you are dealing with a physical Adult..........and an Emotional toddler......
Good luck!!