とき versus 〜たら

The critical difference is that ～たら assumes that the prior action has been completed before the subsequent action begins. Accordingly, a more accurate translation of ～たら would arguably be ‘once’.

仕事しごとが終おわったら有楽町ゆうらくちょうに行いく。(〇)

Once work has finished I’ll go to Yurakucho.

In other words, we can’t start going to Yurakucho whilst we’re still working. One action needs to finish before the other starts. とき, on the other hand, is more flexible in this respect, although for actions that are naturally sequential ～たら is usually the better choice.

仕事しごとが終おわるときに、有楽町ゆうらくちょうに行いく。(△)

When work has finished I’ll go to Yurakucho.

Note also that the tense of the first clause does depend on the relative timing of the action (as it does in English).

仕事しごとが終おわったときに、有楽町ゆうらくちょうに行いった。(△)

When work finished I went to Yurakucho.

For other sentences the difference is less distinct.

駅えきに着ついたら雨あめが降ふっていた。(〇)

Once I arrived at the station it was raining.

駅えきに着ついたときに、雨あめが降ふっていた。(〇)

When I arrived at the station it was raining.

Both sentences are acceptable here because we don’t know when it started to rain, anyway.

At other times the meaning changes substantially.

お父とうさんは新聞しんぶんを読よんだら、ラジオを聴きく。

Once my father has read the newspaper he will listen to music.

お父とうさんは新聞しんぶんを読よむときに、ラジオを聴きく。

When my father reads the newspaper he listens to music.