If a game effect causes an additional effect to occur when you play a gem or relic, you resolve the gem or relic first, then resolve the additional effect.
Example: Arachnos has one charge and Convergence prepped (While prepped, when you play a gem or relic that costs 3$ or more, gain 1 charge). He plays a 3 cost relic, Riddlesphere (Gain 1 charge. OR You may lose 2 charges. If you do, gain 5$.). Riddlesphere is fully evaluated before gaining a charge from Convergence, so the first Riddlesphere option must be chosen (Gain 1 charge).