When does a Summon spell take effect

!st ed: The Summon Monster and Summon Nature’s ally spells all have a casting time of 1 round. My regular group have always taken that to mean that the summoned creature begins to act in the following round. My new group (I’m GM for the first time) is claiming that it should appear and start to act in the round in which the spell is cast. Who is right? Does it make any difference if the caster is actually a Preservationist Alchemist invoking Bottled Ally?