Occasionally when I enter combat with enemies they will throw one or two explosives at me whether they are molotov cocktails or frag grenades. I recently fought the Raiders in Hangman's Hallway and after shooting one of them dead I proceeded to hurl about 4 cocktails into their base. They returned fire by first throwing a molotov at me, then a frag grenade, followed by another cocktail in between their gunfire.
I don't know if my thrown explosives made them more willing to throw theirs or if it was because I was on Very Hard difficulty but I found their seemingly irregular bout of throwing explosives strange in comparison to other enemies.
Best Answer
In my experience, the weapon you use does not affect how enemies counter. Raiders and Gunners are about as likely to throw a grenade at you regardless of whether you're using a Small Gun, Energy Weapon, or Explosive yourself.
What does seem to matter, however, is your position. Enemies don't need move too much when your character is already exposed and you're in their line-of-sight. They may switch to different cover, but that's about it. When you're out of their line-of-sight is when their behaviors start to change up.
What's likely happening is you're taking cover to throw a grenade over whatever object you're protected by. When you aren't visible to an enemy they'll attempt to reposition to outflank you, or they'll try and flush you out with a grenade. I think their grenade-throwing behavior coincides with you taking cover.
I wouldn't outright advise you to remain exposed while you throw your grenades, but it may be safer to throw and reposition rather than wait for an explosive to flush you out of cover.