In short no they do not contridict each other.
A person cannot say he has bitachon and then go and spend money on whatever they want. in fact i would imagine that most people with REAL bitachon live very simple lives and calculate their money wisely.
The chovat halavavot in ??? ?????? ??? ? speaks about the differences between the person who has bitachon and works for his parnassa to the person who works and does not have bitachon. It is worth reading. It would apply to living by a budget as well.