zinzya wo deta ato, syasin wo torimasita.

In Japanese, some intransitive motion verbs like 出る can take を to mark the point of departure or boundary being crossed. For example:

• 家を出る (to leave home)
• 部屋を出る (to exit the room)
• バスを降りる (to get off the bus)

Here, 神社を出る means “to exit the shrine,” and を indicates 神社 as the place where the action starts.

出たあと is a noun phrase meaning “after having left.” It’s formed by:

1. The plain past form of the verb (出た from 出る)
2. Plus あと, which turns that verb phrase into an adverbial time expression

Thus, 神社を出たあと literally means “the time after (we) left the shrine,” marking when the next action (写真を撮りました) took place.

When あと follows a verb to indicate “after doing,” it is normally written in hiragana. The general guideline is:

• Write あと in hiragana after verb phrases (e.g., 食べたあと)
• Reserve the kanji 後 for nouns or set expressions (e.g., 午後, 朝後)

This keeps the verb+あと construction clear and easy to read.

Subordinate clauses (like temporal clauses) in Japanese use the plain form regardless of the overall politeness level. The main clause determines the sentence’s politeness:

• Dependent clause: 神社を出たあと (plain past)
• Main clause: 写真を撮りました (polite past)

Even in polite speech, the clause before a comma or conjunction typically stays in plain form.

Yes, 出てから (te-form + から) is another way to say “after leaving.” Both patterns convey sequence:

• 出たあと = “after having left” (focuses on the time following the action)
• 出てから = “once/after leaving” (emphasizes that the next action happened immediately afterward)

They’re largely interchangeable in everyday use, with only a slight nuance.