Hot water in cold water line

We moved to a new house recently. There was a dead recirculating pump installed on a dedicated return line, or at least that's what I thought the line was as it's a line that connects to the pipe that has a drain valve on the water heater. I replaced the pump and everything seems to be working great, however, in certain bathrooms it now takes about 30 seconds to flush out hot water from the cold water line.

My theory is that hot and cold lines must be crossed somewhere that allows mixing. If the pump was installed on the hot water line at the top of the heater, I understand that I need to cross hot and cold lines at the farthest point from the heater, but is this the correct configuration if the pump is installed on a dedicated return line? I looked under all of the sinks to see if at any point lines are crossed, but didn't find anything. I thought the point of a dedicated return line is to avoid having hot water in the cold water lines.

Thanks for any insight.

GP

Disclaimer... I'm not a plumber

Personal experience with hot water in a cold water bathroom line.

I have a toilet that has a hot water line with a shutoff valve that was put in to feed some hot water into the cold water line just before the toilet tank. It worked to stop the tank from sweating, but somehow it opened a loop of recirculating heat (water?) from the hot water tank through the cold water line leading to that bathroom. As a result, the sinks and tub had warm/hot water for about the first ten seconds. Closing that hot water valve solved the problem, but water condenses on the outside of the toilet tank and drips.

Seems to me that there should have been a way to block heated water from feeding back into the cold water line.

Do you have a check valve for pump cold water will dilute the got by back feeding into circ line all you cold water is on the bottom of tank

I have a check valve on my return line, yes.

The cold water input is at the top of the tank. I have a ball valve, but not a check valve. I was thinking about putting one prior to the expansion tank connection to prevent hot water from going into the cold line. But my problem is that I think it's more than backflow from the tank into the cold line. When I was replacing the water heater and both hot and cold lines at the top were disconnected and valves closed, I was still getting water pressure build up in the return line, as well as the hot water line. That tells me I have a cross somewhere. I've since confirmed with several plumbers that if the return line was correctly configured, I should not need a cross between hot and cold lines anywhere in the house to get the recirc to work. The trick is to find where this cross is (it must be inside the walls somewhere) and cap it.

Thanks.

So yours is set up going to cold inlet or down to drain bib