The DM knowledge object lives on the the SH, and the Indexer serves the data which is why the acceleration happens there. Your searches being prefixed with "ACCELERATE_DM" indicates what it is. Go to "Settings --> Data models" on your SH to see a list, clicking on the first Input Field at the top allows you to filter according to the App context, and if you don't know which App the DM belongs to you can select "All" in this field.
In the "Data models" view, the DMs with a yellow lightning bolt next to them are the accelerated ones. Clicking on the arrow to the left of the DM name expands it to show details, and in there Summary Range indicates how long it's accelerated for. Clicking on "Edit --> Edit Acceleration" allows you to change the Summary Range, and clicking on either the name of the DM or on "Edit --> Edit Datasets" allows you to see the Constraints, usually implemented by Macros or Event Types.
If Constraints are present and implemented through Macros, you can go to "Settings --> Advanced search --> Search macros" to edit them, whereas if Constraints are implemented through Event types you can go to "Settings --> Event types" to edit them. You'd want to at least constrain them to specifying "index=", but more filtering may be needed depending on what's there already. Refer to Search/SPL best practice to guide you.
If you don't have access to any of these Settings views, you'll need to talk to your Administrator to get it sorted out.
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