Is it Common to hire and fire people in lab frequently?
First, it is uncommon to hire and fire people that quickly in almost any context.  Evaluating and hiring good people takes time.  Training people to do anything useful takes time: usually more than two months of time.  What you're describing is incredibly inefficient and, as you note, bad for morale.  It's also bad hiring practice in a small lab to not conduct a group interview with the potential coworkers.  To be frank, your adviser does not seem very good at the HR aspects of running a lab.

However, as a counterpoint, it depends very much on the funding situation.  A new professor, unless they're particularly lucky, may not have very much funding on-hand.  Especially if their funding agencies pay out the award in installments, they may literally have to let people go because the funding has run dry.  To be quite honest, a new professor supporting 2 full-time PhD students and their own summer salary is already looking at an annual outlay of $100k-$150, at least in the US (most of which is tuition, since they're supporting two students through grad school).  Many grant agencies (e.g., NSF) typically award $100k-150k per anum grants.  So they could be scraping very low on their funding and have to cycle through people for that reason (e.g., can afford them for the summer, have to dump them in the fall due to tuition costs).  Funding has been particularly tough the last few years.

Secondly, if they are not sure if they can cover your tuition, but the other professor certainly will?  It's possibly time to jump ship to the other guy.  Currently, having just finished your masters and early in your PhD, this is the best time to do so.  If I were you, I would do the following: 


Talk to the tenured professor to ensure this is a serious offer, backed by grant or internal money.  Inquire about how long currently awarded funds are likely to last.
If the situation sounds good, ask if it would cause any political problems to talk it over with your adviser.  Ideally, you want to do this (they are a reference), but not if it might sink the sure offer.
If it won't ruin the new opportunity, tell your current adviser the situation and ask the same questions (is there money, how long).
If they're comparable, choose the one that seems like a better fit for your interests and your academic security.
If it's lopsided, go for the funding security and find a way to work your research into what you are doing.  To be frank, I would avoid any PhD that you can't get funded for.  If there's not enough money in the area to train you, why would there be enough to hire you when you finish?


Finally, if your adviser takes it personally that you are exploring other opportunities when they can't assure you funding next semester?  Jump ship.  A boss who takes things personally is a bad boss.  I had a great programming intern last summer, who we would have loved to keep as an RA.  Unfortunately, a big chunk of funding was delayed due to Congress playing chicken.  A company affiliated with the university offered four years worth of tuition and stipend, guaranteed.  We do work he is more interested in and we could almost certainly cover him over that whole period.  But the key word is "almost."  I told him that I would not blame him at all if he took their offer (which he did).  I hope he's doing great over there.  If your adviser doesn't have that attitude, it's time to go.