Cold/hot water heater help

Hi guys thanks in advance.especially you frodo😃 . I was replacing a water heater and when removing the supply lines I felt cold water in the hot water outlet and hot water in the cold water inlet . So I assumed a miss connection from previous plumber . I grabbed a 5 gallon bucket and turned water on. Right supply line was obviously the feeder as it should be and the left side released a good amount of water but then stopped.. So I see no problem there . So after I replace the heater and turn the water back on I hear the heater starting to fill up , ok great , but wouldn't you know the cold water ball valve is off. Hot water side is filling up the tank at half the speed of the cold side,when on.. ? Home owner tells me he's been living there for 15 years and had recently started noticing long wait times for hot water in shower. Also he says it happens after a plumber replaced his front yard water valve.. And I notice the meter needle ( triangle) is spooning forward and backward... I'm stuck guys any clues as too what's happening here?? Thanks and ps when I was draining the water heater I was getting good constant pressure with the cold valve off , then it became low when I shut the main off..??

you said, you put a bucket under the cold side

Front water valve is the main shut off valve under the front yard hose bib.. The water coming out the hot water side seemed to be coming out at low pressure .. I also asked some of my company's senior plumbers ,one said there must have been a handle valve open allowing for water to cross over . And another said the shower cartridges might have to be replaced ?i guess I'll start with replacing the cartridges

If there's any single lever faucets in the house, you can get cross over into the hot side and it will fill the tank from the hot side of the cartridges are not posi-temp.

Thanks Matt, homeowner doesn't want to replacing anything at the moment as he is planing a full remodel in the near future

Moen cores are notorious for internal cross over.
Is there a recirc pump on the hot system?
They can contribute to the back flow of hot into cold sometimes.

The main shut off valve is commonly called the SERVICE valve.
They are not always in the front.

Thanks Mr David , I will start using the term , service valve , and there was no recirculation pump.