The "butterfly effect" or "chaos" is the following statement:
"Certain non-linear systems have a very sensitive dependence on
(precision of) initial conditions, so that two identical systems with a
slight mismatch (of the precision) of their initial conditions tend to diverge
exponentially as they evolve though time".
This is the accurate statement of the butterfly effect.
In effect this means that the weather, as an example of such a non-linear system, when predicted over very long periods of time, needs almost infinite precision of the initial conditions to be fed to the simulator in order for the prediction to be accurate. Else the prediction can be accurate only for a short time interval depending on precision of initial conditions used. Thus if during measuring the initial conditions to feed the simulator, some small perturbations are left out (eg the movement of the wings of some butterfly), then the simulator over long period of simulation will exponentially diverge in its prediction from the actual system.
However this is only over sufficiently long periods of time. For adequately short periods of time, the results of the prediction will not be very far off the actual outcome, and this is indeed how weather prediction works.
In other words, no, you lifting the glass and a car accident happening at that time is not related to any butterfly effect as explained above. Trying to find correlations (which do not necessarily imply causation) among events is a process that has pitfalls and one can easily land on "superstition land" if one does not validate the conclusions.