Let’s say I want to describe event model in some software. Conceptually there are two sides: the one which raises an event and another which receives it.
While I do know the difference between to raise and to rise, I’m not sure whether I should say
“rising side” or “raising side”.
As @mplungjan and @MarvMills point out,
trigger is the accepted term.
something that causes something else to happen
If you need to describe code that originates an event, you can just call it the event trigger, as trigger has a noun definition that is well understood and fits within the analogy. Triggerer is clumsy, but should be understood by native english speakers. You can also go with dispatcher, origin (or originator, origin point, originating code etc.) and variations on these.
If none of those tickle your fancy, you can always try a thesaurus.
Programming Exceptions are really just specialized events. Most programming languages use throw-catch for describing these events; while it’s a valid metaphorical description of normal events, I would not use throw-catch language for anything that wasn’t an exception or error handling. Raising is also commonly used for exceptions, so I would shy away from that term as well.
An even older type of event programming is Interrupt driven, which have variously been described as triggered, messaged or signaled. Edge-triggering is a specific term to hardware interrupts; the term you suggest rising-side puts me in mind of the physical signal (voltage), so I would not use that term either.