Cold water supply through water heater?

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We had a recent repipe done by not a great contractor (not my choice, long story).  They failed to strap the pipes so now there is major rattling and pipe contraction noise in the walls where there didn't use to be.  But my biggest concern is that any use of the cold supply at any faucet and the toilet generates fill action in the water heater.  Why would all the cold supply be going through the heater causing it to refill?  I'm so confused.

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@Account Closed They may have reversed the hot & cold.  Was this a licensed plumber?  It also sounds like you're going to have to go back in and secure the pipes properly.  Were permits pulled?  

Good luck with it all.