It's not normal. A vehicle without the factory remote start option should not start with the standard FOB. I'd say your aftermarket remote start is screwed up and interfering. Personally, I'd have the dealer deinstall it and get my money back since it's not behaving as it should - i.e. it's interfering with the factory functions. I wouldn't ever have a dealer install any aftermarket item, especially ones that can be invasive such as a remote starter, car alarm, etc. They usually have a big margin on these items, hence a big markup, and could be using inferior products.