たら and 時 can be used to say "when" expressions. I have learned these grammatical expressions already. In the book みんなの日本語, there is a question that goes...
昼ご飯を a.食べた時 b.食べたら、すぐ出かけます。
When seeing this, instantly I would pick 'b'. However I can't explain to myself why it had to be 'b' when 'a' doesn't sound grammatically wrong. Is it perhaps the すぐ that made it that way?
Because 時 means "the time when" but not "then". The word "when" seems to mean the both.
昼ご飯を食べたら、すぐ出かけます would be translated as "After eating breakfast, (then) I will go out soon."
Does 昼ご飯を食べた時、すぐ出かけます(The time when I ate breakfast, I will go out soon.) make sense?
I guess this is also what @YuuichiTam wanted to say, that ～時 only means literally "the very moment" the verb takes place. When you do something a breath after the action, it is no longer in the expression's scope. For example, you could say:
りんごを食べた時、すぐに腐っていることに気づいた。
When I ate the apple, I immediately noticed it's rotten.一口食べた時、すぐ懐かしい記憶が蘇ってきた。
A bite of it immediately brought me back memories of good old days.
Likewise(?),
昼ご飯を食べた時、すぐ出かけます。
would perhaps mean that when you put the last piece of meal into your mouth, you suddenly find yourself outside the door. That's pretty futuristic. But if you want to follow the traditional method of putting the fork down and walking from dining table to entrance on your feet, you must say:
昼ご飯を食べたら、すぐ出かけます。
昼ご飯を a.食べた時 b.食べたら、すぐ出かけます。
Is it perhaps the すぐ that made it that way?
I think you are right. The two words are connected each other very well as ～したらすぐ to us.
したときします has a notion that you are just waiting for that occasion. We don't use this expression for things we are up to now.
It works if it's 昼ご飯を社食で食べたときに（給仕さんに話してみます, etc.) because it says 社食で, and we say this when we don't really know when we eat at the office cafeteria. Without any adverbs like 社食で, 昼ご飯を食べたときに alone is almost like saying you eat lunch not everyday.
