"Don't take a decision that/which is based on your assumptions." is more expected. "that is" and "which is" are likely candidates for omission in that context in particular.
Your second version, for clarity, is "Do not take a decision when/while you are based on assumptions" or similar wording. With as subject the person addressed to, and as object "your assumptions". Thing is, "your assumptions" is an indirect object.
"A bases X on Y" has A as subject, X as (direct) object, and Y as indirect object. You cannot say only "A bases on Y"; that's got something missing. You have to base something on Y.
In regular usage, "base on" requires both a direct and an indirect object; else it is awkward or even indirect grammar. So, in "Don't take a decision based on your assumptions" only has both object types if decision is the direct object, and assumptions the indirect one; leaving out the subject. It's an abbreviation of the passive voice, you're saying "a decision which has been based on your assumptions - don't take it". The subject in the passive voice is left ambiguous - it does not have to be the person addressed to in this imperative sentence. You can imagine a scenario where someone else designs a decision solution, based on your assumptions, and you are to take it. Not likely in practise, but grammatically probable.
The other explanations either leave out the direct object, or they base the person addressed to on assumptions, and you cannot base a person on assumptions. So they are wrong.