"hold these for me until I get there" is exactly the same as "don't let someone else buy them before I get there". Whether you pay before you get there or after doesn't change the fact that the item is being held for you so that no other customer will be able to purchase the items that you ordered.
We can break down your two statements and put them piecemeal side by side:
I assumed they meant... "hold these..."
What I am saying is... "pulling the items from the shelf..."
You're completely correct. What I was trying to communicate, and what I should have emphasized, is that it's not just a send and forget kind of process. After the items have been set aside you get an email/text to confirm that things are ready to pickup and in my experience everything that I've ordered is there when I go to pick it up. So I'm saying that the things that were listed as in stock on the website are actually in stock at the store, and I get a confirmation once everything has been "secured" for me.
We can break down your two statements and put them piecemeal side by side:
I assumed they meant... "hold these..."
What I am saying is... "pulling the items from the shelf..."
I assumed they meant... "at the counter..."
What I am saying is... "in a special area..."