The use of comma in these sentences

Thus, the differences between the critical and average delays for BCLAs and KSAs are small, and, consequently, RPTs in multipliers with BCLAs and KSAs should be easily detected than those in multipliers with RCAs according to the above conditions.

Operationally, collective behavior was detected and quantified using correlations or, more recently, by mutual information estimated either locally or globally.

My issue: The above two sentences have " and, consequently, " and " or, more recently, ". I understand that commas are used in long compound sentences or between independent clauses joined by a coordinating conjunction. After the conjunction "and" and "or", consequently and more recently are followed by a comma.

Is this normal for any transition or is it a grammar error?