Another plumbing question

I'm guessing only pros will know the answer to this one.

I replaced a reverse osmosis under sink water filter with a simpler single canister non-RO filter (made by the seemingly well regarded CuZn company).  Per the manufacturer's direction, I connected the old plastic tubing that was part of the RO system to the brass tee connected to the water supply.  The water pressure coming through the plastic to the drinking water faucet and the fridge (the tubing splits to feed both) is now much stronger than it was with the RO system.  Should I be worried about the affect of the pressure on plastic tubing?  At various junctures, sections of tubing connect via plastic fittings with slide-in collars.  They always struck me as rather flimsy although I never had a leak or flood in the 15 or so years of using the RO.  Should I be worried, and should I/can I do something to lower the pressure?  

(not a plumber) if water pressure inside home is too high, plumber can install a device at the water meter to correct that.

Regardless I’d suggest replacing 15 year old plastic tubing at this point. 

Probably a better, more direct way to plumb this. 

Thanks.  I already have the pressure control thing where the water comes into the house.  I checked earlier and the PSI was under 60, which I think is pretty mild.  Still, they eye test says the water is coming out real strong from the water faucet.  Maybe new plastic is a good idea.