- It is updated automatically.
- It is automatically updated.
- It updates automatically.
- It [ ] automatically updates.
We can put adverbs of manner such as automatically either at the end of the verb phrase or after the auxiliary verb position. In sentence (1) we see the adverb at the end of the verb phrase. In sentence (2) we see the adverb after the passive auxiliary BE. Sentence (3), like sentence (1) has the adverb at the end of the verb phrase. In sentence (4) there is no auxiliary. However, we can still understand where the auxiliary verb would be, if there was one. It would go where the brackets, [ ], are. So in sentence (4) we still see the adverb after the auxiliary verb position.
However, sometimes there is more than one auxiliary. For example in the sentence:
- It will have been updated.
Of course we can put the adverb at the end of the verb phrase here:
- It will have been updated automatically.
But we can also put it after any of the different auxiliary verbs. Here there are three auxiliaries. There is the modal verb WILL, the perfect auxiliary HAVE and the passive auxiliary BE. The adverb can go after any of these auxiliaries. Each possibility is as good as the others. They are all good and perfectly natural English:
It will automatically have been updated.
It will have automatically been updated.
It will have been automatically updated.
You can choose which one sounds best to you!
The Original Poster's example:
- Note the context variables can be automatically updated ...
- Note the context variables can automatically be updated ...
Here there are two auxiliaries: the modal verb CAN and the passive auxiliary BE. The adverb can go after either one. Both patterns are very common and perfectly acceptable. The writer could also have written:
- Note the context variables can be updated automatically ...
Here the adverb comes after the verb phrase. This is also a fine option. It's good to have choices!