In your case, if your lab or unit is using a convention that's not standard in your field the most straightforward solution is to make a note of this in your articles.
The answer is strongly conditional on discipline and, to a lesser extent, country of origin. Conventions vary widely, as does the degree to which they are institutionalized. For instance, in some fields (e.g., Philosophy co-authorship is not common and there is no convention about attribution, so absent an explicit note people are are likely to think the more senior author. Even worse, there may be a kind of hermeneutics of author-order where people parcel out credit to different contributors regardless of order of authorship, as when someone says "Sure, X is the first author and Y helped him write it up but it's obvious the paper was Z's idea". But other conventions exist, too. Knowing what they are and how to interpret them is part of one's socialization into a discipline. To make things more complicated, some fieldsor some journals, or some labs, or some individual authorsmay have their own rules or conventions designed to clarify things by listing credit more explicitly.