When my newly installed heat pump comes on , the outside unit and the inside blower come on at the same time causing the lights in the whole house to dim. My electric service and lines to units are adequate. Seems like the blower should wait for the coil to warm before kicking on! Is this normal?

Yep, it's normal for the inside blower to come on immediately with heat pumps. As far as the dimming, you may want to have an electrician do a check on your panel for it's capacity , and for loose connections.