た is not 'yesterday'. It is a stamp already down.

Where the picture shows up in た形

1. 1

   a mark left behind

   日本に来たのは去年です。

   nihon ni kita no wa kyonen desu

   It was last year that I came to Japan.

2. 2

   the mark of having tried it

   富士山に登ったことがあります。

   fujisan ni nobotta koto ga arimasu

   I have climbed Mt. Fuji.

   For experience it is always た + ことがある.

3. 3

   a mark just stamped

   今、駅に着いたところです。

   ima, eki ni tsuita tokoro desu

   I've just arrived at the station.

4. 4

   the stamp you'd better have

   薬を飲んだほうがいいですよ。

   kusuri o nonda hō ga ii desu yo

   You'd better take the medicine.

   ほうがいい normally takes た: 飲んだほうがいい, not 飲むほうがいい.

5. 5

   the mark you were hunting for

   あ、ここにあった。

   a, koko ni atta

   Ah, here it is.

   You use た even though you found it this second — the searching is what ended.