Hmm... I don't think that's what's happening, but allow me to please explain my opinion.
Godzilla isn't the type to 'chase' an enemy. I think that night scene with the flares is just the soldiers trying to figure out what the hell Godzilla is. I think that this scene is probably part of the 1999 sequence and is his first major appearance on land after swimming between the ships and causing the tidal wave in the trailer. The soldiers are likely just trying to light him up so everyone can see him in the darkness and figure out what he is so they can start working on trying to bring him down.
That's my opinion anyway.
I don't believe Godzilla is going to 'chase' the Mutos. There has been no confirmation that there is any kind of deep link between the two outside of the metaphorical. Honestly speaking I doubt Godzilla will share any relations with the Mutos whatsoever, and that the 'link' between them is, in my opinion, nothing more than the idea that they possibly share a point of origin in the nuclear realm. But outside of that, I doubt there's going to be any significant link between them that would cause Godzilla to 'chase' the Mutos.
But again, this is just my opinion on the matter.