How did this action have that consequence?

In the last episode of Life is Strange, Max goes back to

the beginning of the first episode and alerts David to Jefferson's crimes and hideout.

Returning to the present,

we see that Jefferson was arrested soon afterwards (the photographs of that replace ones that took part during the intermediate episodes) and so in the present Max is not his prisoner.

Later,

Max goes even farther back and tears the photo that would be her submission to the contest, intending to make sure she doesn't leave Arcadia Bay. But somehow the result is that Jefferson hasn't been arrested, and it's only after she's already a prisoner that David finds his hideout.

I don't understand how Max not having a photo to submit delayed David finding out about Jefferson. David said Max led him there, which implies she still sent that message in the altered past, but this time around David gets there several days later.

How did altering that bit of the past delay the rest?

Solution 1:

Max originally

escapes the dark room

by using her diary. After she

pleads with Jefferson, he

tosses the diary at her and it opens to the page of the photo she took in class.

By tearing up her submission photo

Jefferson became mad at her (because he thought she was talented and by not submitting a photo he felt she was just wasting it) and

burnt her photos and diary. This meant that the timeline played at like it first did, except she wasn't able to

escape the dark room anymore because she didn't have that picture to look at. Since she wasn't able to escape, she wasn't able to warn David.

As revealed in Episode 4, David actually had surveillance of the place, so it's conceivable he was just able to figure it out for himself

seeing as Max and Chloe were both missing (I assume they weren't missing for long, and this may not have contributed to him solving it)

Solution 2:

Before Max

went back in time and handed Jefferson the photo for her submission,

She

texted David, warning him about the Dark Room.

So,

when Max tore up the photo, she didn't change the fact that she texted David, because she did that before handing in the photo.

Max left evidence of her investigation,

whether you wanted to or not. It is possible that David routinely investigates the barn and/or has it under surveillance, but didn't find anything. However, Max brushing away part of the floor showed David where to go.

This way,

Max "led him here." The text put the barn under surveillance, and the uncovering alerted him that something was going on.