The 3.5 gpm specified, is not related to the injector.
The injector acts as a venturi to draw brine from the brine tank. As a #2 Blue injector is the proper (usual) size for a 12" or 13" diameter tank, the water flowing through the injector during the BD phase of the regen cycle, will be 0.84 gpm, which will create suction on the brine port to draw brine at 0.56 gpm. Once the quantity of brine lowers to the pickup screen in the brine tank, an air-check valve (floating ball) closes to prevent air from being drawn into the system. The 0.84 gpm injector flow continues to rinse the brine through and off of the resin, out of the resin tank. Brine is usually all drawn within 15 minutes while the remaining 45 minutes of the 60 minute BD setting is used for the slow rinse.
The 3.5 gpm relates to the 'drain line flow control' (DLFC) button installed in the drain port. The DLFC resembles a washer with a specific size hole which the drain discharge flows through, limiting the rate of drain flow. That rate corresponds to the amount of flow required within your 12" diameter tank, to lift the resin during backwash (5 minute BW setting) and flowing downwards during Rapid Rinse.
Backwash causes the resin granules to be loosened to permit debris to be flushed away and also to provide more complete contact with the brine. The Rapid Rinse will repack the resin tightly so that service flow is forced to flow through the resin bed instead of the spaces between the granules.
Edited to ask: Does the label specify a #1 injector is installed? If so the flow rates for the #1 White injector would then be 0.45 gpm rinse and 0.38 gpm brine, which MAY require a longer BD setting.
Now that you have set the appropriate BF setting, it would be good to be in attendance during the next regen cycle to measure the time required to draw all the brine from the brine tank. That should be 1/4 of the BD setting to be programmed.