Hot water back feeding to cold from new water heater

[gor32]

Just installed heat pump water heater and am getting warm water in the cold taps. The water comes into house, splits to softener, then back, then to wh, then cold taps. The hot in the cold lines makes it all the way through the expansion tank and then up into ceiling. According to Rheem there are no heat traps in this heater.
I am thinking of either adding heat traps or a one way valve before the expansion tank.

Any other ideas on what is going on and how to fix it?
The old tankless is still there and would work if not shut off (backup) but I wanted to get got water off of my propane.

I am looking to have as little added restriction as possible because right now I have no water pressure in either shower and am planning to do a shower remodel with a couple body jets. I believe this is a separate but coincidental timing, but oddly enough the water pressure in the up stairs shower dropped to almost nothing when the wh was replaced. That was with trying to use old or new wh. The down stairs shower had not worked since we moved in but I just assumed it was a bad shower valve because the bathroom faucet works just fine. I only added one 3/4 pex tee between the old wh and the house so that's what makes me think timing is just coincidence (barring a small chunk of gunk plugging up the shower hot).

 

[gor32]

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[MrInfoPhilly]

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Do you have a hot water return pump on?
If so, IS there a check valve

 

[breplum]

There is nothing about a heat pump WH that would affect mixing unless connected incorrectly.
What is that black hose connected to side tap midway up the HP tank?
A common source of mixing can be a bad shower valve. The Kohler K304 series are well known to me to go bad and mix.
The first thing to do to check that there is no cross connection is to turn the cold water supply at the WH "off". Then open hot water tap anywhere in the house. After depressurizing, there should be NO flow out of hot water taps unless you have a cross connection somewhere.

 

[MrInfoPhilly]

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He never responded., but I'd bet he has a line crossed. So many pipes and tees going into the inlet., all the same colors. Its hard to see whats what. Take a picture far back so we can actually see what we are looking at and how its tied in

 

[wpns]

What is that black hose connected to side tap midway up the HP tank?

Condensate drain?