Your system is obviously much more than just an acid neutralizer and softener.
The control valve shown for the acid neutralizer (AN) is a Fleck 5600 mechanical Filter valve with 12-day skipper dial. The 5600 has a limited drain flow rate so it is not the best valve for an AN application, but it appears to have been in place and utilized for that application for some time. You didn't specify the tank diameter.
Perhaps by saying "after company added neutralizer", you actually meant they added additional media to the exsisting tank, not a newly installed neutralizer as I had initially assumed.
The 5600 is shown equipped with a 2-handle bypass valve, and each control valve is likely similarly equipped.
The current time shown on the front of the 5600 is almost 3pm. Is that the correct time when you took the photo? If not, view the window on the back of the timer motor to verify the motor is actually operating. If the motor is not operating, the unit will not backwash which will lead to the media becoming compacted within the tank which will result in a flow restriction through the media.
Assuming the motor is operating, restore flow through all treatment devices and check the flow to home faucets. If flow continues to be restricted, bypass only the AN to determine if there is any flow improvement.
If the flow has improved, thereby confirming the AN is causing the restriction, unbypass the AN and manually turn the front control dial to the Backwash position to initiate a manual backwash cycle.
Once water is flowing to drain, unplug the AN's electrical power plug to allow the backwash cycle to further continue longer than usual. After allowing the unit to backwash for 30-minutes, restore electrical power and permit the unit to complete the remaining backwash cycle itself.
Once the control dial has returned to the 'In Service' position, test the flow rate to faucets to determine if flow has improved.
Although not fully visable, it appears the skipper dial tabs maybe pulled out inconsistantly so backwash is programmed to occur sometimes after 2-days, and sometimes after 5-days. Suggest resetting the tabs so a backwash cycle will be performed consistently every 2 or 3-days.