It's not unusual for the engine to need 20 or 30 seconds of cranking for a cold start, particularly in winter. If it is the same for a hot start, such as after filling up with petrol, then you might have an issue.
The tuning upgrades shouldn't affect the starting.
Personally I never found cycling the ignition before starting to make any difference, just wait until the fuel pump noise stops before cranking.
How old is the car and which battery did you replace the Exide with?
