If you are of the LDS (aka Mormon) faith, you will also notice that in the weekly church meetings, the blessing of the bread and water (specifically the blessing of the water) also uses the same structure. I've included the direct quote to show that this is not an isolated usage
... and witness unto thee, O God, the Eternal Father, that they do always remember him ...
I think that the greater context of this translation is that with regards to the future, the intention is that the individual who takes the sacrament will show that they always be in the state of remembering him (Jesus).
For future tense, as you are probably well aware, there isn't a specific grammar that you can use. Additionally, as this source notes:
Grammatically, Japanese does not have a future tense in the sense of a verb form reserved strictly for the future. However, that’s because the whole idea of present tense is ambiguous. It’s more accurate to say there is no present tense and the plain form is the future tense in addition to other usages. What we commonly think of the present tense as expressing what’s happening now is really the present progressive which Japanese clearly has in the 「～ている」 form.
So how is this phrase future tense? The answer all relies on the verb that is actually happening in the sentence, 証明する.
覚えている is followed by a nominalizer, こと. This turns
the thing of remembering. From this point, we can pretty much treat it as a noun, but the translation can sometimes get sticky.
Now adding on 証明する, we get:
witness that (you) will be in the state of remembering
The action verb is witnessing (証明する).
Adding いつも should be a simple jump to:
always witness that you will be in the state of remembering.
That sounds a little wordy, so rewording the English:
witness that you will always remember
Notice that in the English translation, your action is not remember, but witness. Because of that, the 覚えている in this translation is expected to continue occur in the future.