The expanded spell list tables are arranged by spell level.
The spells included in your expanded spell list table are considered to be included in the warlock spell list for you according to the given spell levels. The levels shown in the expanded spell list are not character or class levels. They are spell levels, as indicated in the table header.
This means that the 1st-level spells in your expanded list are added to the 1st-level warlock spells you can learn, the 2nd-level expanded list spells to the 2nd-level warlock spells you can learn, the 3rd-level expanded list spells with the 3rd-level warlock spells you can learn, and so on.
You become eligible to learn any of the spells on the expanded list of a given level precisely whenever you would be eligible to learn a standard warlock list spell of that level, which is indeed whenever your warlock spell slots are that level or higher.
So, for example, the 3rd-level spells listed in the expanded spell list are considered to be included in the list of 3rd-level warlock spells for you, meaning that you are able to learn them when you reach or exceed 5th-level as a warlock and become eligible to learn 3rd-level warlock spells in general.