Can a druid's "Giant Insect" attack immediately upon casting?

Question

The level 4 Druid spell "Giant Insect" reads, in part:

You transform [some arthropods] into giant versions of their natural forms... A centipede becomes a giant centipede [etc.].

Each creature obeys your verbal commands, and in combat, they act on your turn each round...

Do the giant bugs attack immediately?

The Rules-As-Written make me think, "Yes". The hobgoblin that was queued to go next in initiative order will just have to wait while this giant centipede chews his leg off.

The spell description is not explicit on this detail, though.

Here's the problem: A round is six seconds (ah, how things have changed since first edition!), and it's understood that I'm using a sizable chunk of those six seconds when a spell's casting time is "One Action". When the wizard casts "Fireball", the hobgoblins cook at the END of the casting, not the beginning. Surely the giant insects don't appear until their turn (my turn) is over?

I can think of three possible interpretations:

1. The insects get their full turn immediately because it's a game, and this is just a competitive advantage "Giant Insect" has over "Conjure Woodland Creatures" or "Conjure Minor Elementals" (both level 4 druid spells).
2. The insects get their full turn because it's MAGIC! The insects retroactively appear and attack when the druid starts his or her turn, or maybe they grow with their stingers already driving toward their victims' torsos. We're already violating the laws of physics with magic; a few seconds of time travel isn't something to get choked up about.
3. The insects appear at the end of the druid's turn and have to wait until the druid's next turn before they can eat the hobgoblin. Again, magic violates the laws of physics, but since the rules don't explicitly say when the physics-defying bugs get to attack, we only let them attack when the laws of physics say they should.

Answer 1

Assuming you cast the spell on your turn, yes they should be able to act immediately

Each creature obeys your verbal commands, and in combat, they act on your turn each round.

After you cast the spell, the insects are able to act on your turn whenever that occurs. If you cast this spell on your turn, then the insects are able to act as part of that same turn. After all it does say "each round" and there is no reason to think that the turn that the spell is cast in is excluded in any way.

If you do cast the spell when it is not your turn (for example, by taking the Ready action), then the insects would act whenever your turn next comes up.

Using assumptions about time is not going to help understand the rules

Jeremy Crawford has said:

A round in D&D lasts for about 6 seconds. None of the things that take place during a round—actions, movement, and the like—have official amounts of time assigned to them.

It is a bit of a trap to start thinking of things in terms of how much of the ~6 seconds any given action takes because it is not going to make sense really. The rules of 5e are not meant to have each thing you do translate into any realistic time estimate. So, there is no real way to try to judge or make sense of the rules using time as a measure.

The rules dictate that all the actions of all the creatures in the combat add up to "about 6 seconds" no matter how many there are or what they do. Even though it doesn't really make sense it is true because the rules say it is.

Thus your statement

it's understood that I'm using a sizable chunk of those six seconds when a spell's casting time is "One Action"

is not necessarily true. And even if it was, is not going to be helpful in adjudicating the rules.

In this case, the answer can be read directly from the spell effect.