12 V across 10 ohms is only 1.2 A. A more likely cause is the back EMF spike when the contacts open. There is an R-C snubber in there, but this thing was designed way before switching or other regulated supplies. A fast diode directly across the coils, like a Shottkey or a tranzorb, would be better protection. However, this now makes the device polarity-sensitive. Placing the diode across the power supply output still lets the spark happen across the timer contacts, but should be enough protection and it doesn't force polarity sensitivity onto the device.
ak