After one round of minor revision, my submission has now reached the "Awaiting EIC decision" stage. In the meantime I just wanted to get some insight on what this entails. Do editor-in-chiefs usually follow the recommendations of the associate editor below them who managed the review process?
For a journal large enough to have multiple layers of editors, the EIC is unlikely to be directly involved in the processing of most articles. Depending on the journal policy, the EIC may be formally required to approve all publications, but this would be a pro forma step in ordinary circumstances. For some large journals, the an article may never cross the EIC's desk at all if there are no problems during the review process.
When the EIC would become involved is if there is a problem. I think this would normally occur when an author protests against a rejection. However, it is conceivable that an associate editor might escalate a problem that occurred internally, if there was some peculiar problem with the submission or the reviews.
In your case, if you are not aware of any unusual circumstances surrounding your submission, I would assume that the EIC will follow the judgement of the associate editor.
TLDR: journals have their own procedures and understanding what is happening in your case will depend on the journal's processes.
Allow me to detail two opposing processes, each involving two different journals I continue to advise. Both are non-open access journals that have been in operation for decades.
In the first journal, published fortnightly, deputy editors gather twice a week to discuss the manuscripts under preparation. During these meetings, the Editor-in-Chief is almost always present. Each of the deputy editors presents each manuscript under his or her care, with a recommendation to the group. There is brief discussion and consensus is reached. The Editor-in-Chief generally accepts the decision of the group, but there are times when he has overridden the consensus. The deputy editors always inform the authors that the decision has been reviewed by the Editor-in-Chief and all deputy editors.
In the second journal, published six times a year, deputy editors work with more independence and only call on the Editor-in-Chief when red flags arise.
In the end, there are more processes than there are journals (mainly because workflows change all the time even in the same journal). Trying to read into a statement in the email is like divining from tea leaves.
It is generally the case that deputy editors are happy to describe the editorial process to authors. I suggest that you might wish to contact the journal directly and seek clarification about what to expect. Make sure you read the journal website, though, because it might be explained.