Taking into account the rulings on Summon Limit (the card with the closest effect to this one, as far as I know), which does count the Summons already performed during the turn and before the Trap Card was activated, plus considering that this card specifically applies after the third Summon of the turn and apparently disregarding if this card was present or not during the previous Summons (as in, this card being activated after the second summon of the turn won't change the fact that said Summon was still the second one of the turn, if that makes sense), then yes, this card should also count the previous Summons, unless Konami drops a BKSS/exception ruling
After yelling to his partner not to touch the table while he searched for a card case, Michael updated the Magic: The Gathering subreddit with the good news
"Magikey Mechmusket - Batosbuster" and "Cyberse Sage" are the only Tuner Ritual Monsters
Very little detail was put into the story about the location, so not much was known about it
Normal Deck 6.2 16 [22529] JP166 Arsenal Summoner Effect Monster Flip Monster - 4 Spellcaster 1600 1600 FLIP: Add 1 "Guardian" card from your Deck to your hand, except "Celtic Guardian", "Winged Dragon, Guardian of the Fortress #1", "Winged Dragon, Guardian of the Fortress #2", "Guardian of the Labyrinth", or "The Reliable Guardian"
Look at all the great mid-game cards this deck has