In Terraria, is there an order in NPC appearance in addition to the minimum requirements for each one?

During the daytime of 15 minutes, only 1 NPC can spawn every 2 minutes, the NPC must not exist yet and the necessary conditions (separate houses, …) must be met. If multiple NPCs are eligible, then only the first eligible will spawn. It is checked in the following order:

• Guide: No conditions.
• Merchant: House, players have more than 50 silver together (in their inventory).
• Nurse: House, used a crystal heart.
• Arms Dealer: House, carry a gun in your inventory.
• Dryad: House, must have killed a boss.
• Demolitionist: House, Merchant, explosive material in inventory.
• Clothier: House, Skeletron killed.

Exceptions to the single NPC rule, which spawn before the order given above:

• Second Merchant: House, at least 3 players having more than 10 gold together.
• Second Nurse: House, at least 3 players having 20 hearts (i.e., 400 combined health or more).
• Third Merchant: House, at least 5 players having more than 5 platinum together.

There is no order in which they spawn over time. But they can't spawn together, thus first in order…

First off, I'm assuming there is a free house. According to the wiki, you may want to throw it.

He arrives once you obtain a Dynamite (or Bomb) for the first time and have a house available. The object doesn't need to be used, it only has to be in your inventory. If you have multiple bombs and a house set up and the Demolitionist doesn't arrive, use at least 1 bomb and he should arrive shortly.

In the comments for said wiki page, people mention throwing it and he arrives.

There shouldn't be an order in which they arrive. If you have the requirements, they come. Perhaps this is a bug, or the demolitioniost also needs 50 Silver to come (but nobody never noticed)

I'll try this out this evening when I'm home