No, a company match on dividends is not normal.
So are you sure that it's actual a company match on dividends? Or is your statement simply telling you that the
source of that subset of dividends is from funds that were purchased with company matching money?
In my Vanguard 401(k), for example, if I hold $20k of VINIX, I might get a $100 dividend. But if I tell Vanguard to show the transactions "By Source", it will break that $100 transaction into 4 lines, showing the "source" of each part of that $100 dividend. For me, these four sources are EMPLOYEE PRE-TAX BASIC, EMPLOYER MATCHING, PRIOR PLAN MATCH, and 4% ANNUAL PRE 2014. If $15k of my VINIX holding came from my contributions (EMPLOYEE PRE-TAX BASIC), and $5k came from the company match contributions (EMPLOYER MATCHING), then Vanguard would show that $75 of the dividend came from EMPLOYEE PRE-TAX BASIC and $25 came from EMPLOYER MATCHING. So that $25 isn't new matching money, it's simply a part of the dividend payment.
Here's a thread on the same topic, where everyone agrees that they've never heard of a company match on dividends before, and it's only the last post where someone finally mentions that the OP's interpretation of their statement may be wrong, but the OP never comes back to confirm:
http://www.early-retirement.org/forums/f28/401k-employer-match-on-dividends-69851.html