Although all the cards in The Brothers' War that create Powerstone tokens create a tapped Powerstone token, entering the battlefield tapped isn't part of the token's definition. Notably, if you create a token that is a copy of a Powerstone token, the token copy won't enter the battlefield tapped.
If the card you exiled with the first ability is an instant, you may play it during your end step after Visions of Phyrexia's last ability has already resolved and created a Powerstone token. We call this having your cake and compleating it too.
Powerstone tokens are a kind of predefined token. Each one has the artifact subtype "Powerstone" and the ability "{T}: Add {C}. This mana can't be spent to cast a nonartifact spell."
Magic: The Gathering · ™ & © Wizards of the Coast · Illus. Dominik Mayer
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You must follow all normal timing rules for a card you play using Visions of Phyrexia's first ability and, if it's a spell, you must pay its costs to cast it.
You can use the {C} added by a Powerstone token on anything that isn't a nonartifact spell. This includes paying costs to activate abilities of both artifact and nonartifact permanents, paying ward costs, and so on.
If you played a card from exile for any reason, the ability won't trigger, even if it wasn't the card you exiled with the first ability.
