Assume you're a caster in AD&D 2e with the ability to cast Monster Summoning I, and your game rolls init on a per-round basis. When you summon a monster on a round, does your monster roll init to attack that same round, or can said monster not attack until the next round's inits are rolled?
Short version: It's all about the interpretation of "within one round of casting" in the spell description, and the DM's word is final.
The start of the spell description for AD&D 2e Monster Summoning I says:
Within one round of casting this spell, the wizard magically conjures 2d4 1st-level monsters...
The only thing we can be sure about in terms of the AD&D 2e rules is when the spell is cast, taking into account your party is using individual initiative for PCs.
The spell's casting time is given as '3'. This is added to the spellcaster's intitiative roll to determine the place in the round when the spell is cast (See PHB Table 56: Optional modifiers to initiative).
So far so good.
Now "within one round" from the spell's description is open to interpretation, and as far as I can tell is not further specified in the PHB or DMG.
In AD&D 2e, the smallest unit of time for practical purposes is a (combat) round which is defined as "approximately one minute". (AD&D 1e further subdivided a minute-long-round into 10 segments of 6 seconds - see AD&D 1e PHB 43 - but this unit of time is not explicitly defined or referred to in the AD&D 2e books, and only survives in the casting time for many spells as a number to be added to initiative.)
As far as this goes, "within one round" could be interpreted as...
- at the end of the current round,
- at the beginning of the next round,
- at the point of the next round just before the point the spell was cast in the current round (so if the initiative roll was 3, +3 for casting time = 6, the monsters would be summoned on initiative count 5 of the next round.
...and more besides.
In each case your question about whether the monsters need to roll initiative stands.
I think the only help the official rulebooks give us here is of the type given about deviations from the normal combat sequence. The normal combat sequence is: DM decides on his characters' actions, PCs do the same, roll initiative, attacks in initiative order.
Parallel passages in the PHB and DMG say:
The above [combat] sequence is not immutable. Indeed, some monsters violate the standard sequence, and some situations demand the application of common sense. In these cases the DM's word is final.
It seems to me that summoning a monster is "violating the standard sequence" as a monster enters combat having missed the chance to declare its intention. So it seems that it is up to the DM to decide what happens here.
(Subjective footnote: When I was 12 and DMed AD&D 2e games I went for monsters-summoned-immediately-and-attack-straight-away. If you need a precedent for this interpretation, see Summon Swarm, where the swarm immediately inflicts damage with no mention of initiative, but I can't even pretend this interpretation is canon!)