it's a bit low. Does not mean you over-dried. The resulting RH without anything to control it will vary... some people may be luck where it reaches equilibrium at 55-62%, but if it doesn't you need some 2-way humidity packs.
I'd suggest boveda 2-way RH packs. Do not buy 'integra boost' 2-way packs. They do not maintain RH as stated, but the boveda are consistent and dependable.
It'll be irrelevant if you smoke the buds within a few months, but better to maintain a ~55-62% RH and 60s F. Exactly what 2-way pack you want is personal preference. The longer you store the buds, the more sophisticated you want to be about storage.
While 'burping' jars, if necessary, you only want them ~75% filled. Once the RH and moisture content is steady, you want to fill them up 100% -- air and heat are your enemy but light is your biggest enemy to long-term storage.
moisture isn't 'allowed in' if your ambient RH isn't higher than the stated "51%" ... so that depends on your local weather. This is why a 2-way RH pack makes life easier.
moisture reader, if accurate, is probably the best way to pay attention. I think 13% is still higher than normal, so you'll have to burp for a while.
At 60-something F and 60% rh, based on bud density and other variables, some resulting moisture content will result. This is where you'll see variation... larfier stuff will likely have a lower moisture content in same conditions than denser buds... the rate of evaporation is faster with increased surface area and less density. could be wrong... but it's an educated guess.
Some random site says:
https://www.truelabscannabis.com/moisture-content
6-9% is optimal and most should fall between 6-15% ... so you could be fine, according to this web site. This was a cursory search, and i would google for more sources to verfiy whether it is good information or not. From what this says, the important part is staying under 15% to avoid microbial growth.
Since you have the ability to measure moisture content of the plant material, it's going to be the best way to dial the process in.