who told you this?  the installer?

yes, take it back and tell them to fix it.  they've messed up one of the
earthing circuits.

The dome light is indeed routed through the factory radio in '96 - '98
Civics. This is because on models with a security system, the control
unit is inside the stereo, and the security system is using the dome
light wire to monitor if any doors are opened.

The problem gets worse if you have remote keyless entry, as the factory
receiver for this is also inside the factory stereo.

Since you only are missing the dome light, the solution is easy. Get
part number Part Number HA03B from http://www.scosche.com/ and plug it
into the now unconnected alarm / keyless entry plug behind the stereo.

If you feel adventurous, you can do without the Scosche adapter. Just
locate the connector inside the dash and short together the LT GRN/RED
wire (from door switches) and the LT GRN/BLK wire (to dome light)