Laser firing 2 dots out of the brand new tube

That should not matter - the lense should “center” the beam to the focal point. The problem is, if the nozzle is in the way. At the focal point ALL the parts of teh beam come together to one point, so there’s no reason for the beam to be splitted.

Edit: I’d try to focus the beam, what does it on the surface. If both of parts are parallel, they should meet at the focal point anyway. Of course it’s not good, if the new tube makes weird beam.