No ability to choose which mana from the pool would be used.
Arena of Glory's mana is prioritized, even if other read mana is available. Tapping the land manually or leaving it for automated resolution still forces the "haste imbued" mana to be used first. Meaning - if a player wants to cast three creatures, the first and second will always get haste, and third will never get haste.
"Autotapping" toggling option isn't relevant here. Please make mana already in the pool NOT automatically consumed