I would have the poster mounted to a substrate before attaching it to the frame. foamcore is a good choice if the poster is not valuable. Acid free materials are worth the extra money if they are in contact with the poster. If you mount the paper poster to the wood frame it will never look very good. It will show the frame elements through the paper and the glue will cause differential shrinkage and buckling. If this is just a digital print that could be replaced this is what I would do; mount the poster to foamcore with spray adhesive taking care to avoid wrinkles. Mount the foamcore to your wood frame with double stick foam tape around the entire frame including cross pieces. This will keep the poster from showing the frame members though the paper and will Make an attractive presentation for a year or two. If you value the poster as an artwork, it is irreplaceable, have it done by a professional framer with good materials.
@iLikeDirt covered a lot of important information, but I'd like to add something since the majority of the information assumes that there is a problem of excess moisture due to the concrete, while the expert assessment says it is actually dry cupping that is the problem.
Dry cupping implies that the interior humidity is dropping below the average frequently enough that the wood surface dries out. It sounds like they are suggesting that the vapor barrier between the slab and floor is probably doing its job correctly.
One way to help prevent this is to bring the wood into house and allow it to be exposed to the air within the home so the moisture content is similar to that within the home (acclimation). I like to assume this is standard practice and this was already done, but if you're using a special reclaimed antique pine wood, then maybe a longer period would have been desirable. Major seasonal humidity variation can still have an impact.
Do you know if there is a period during the year where it seems more prominent, or has it not been long enough? If I had to guess, it could be during the summer when the AC/dehumidifier is running more frequently. I'm not as familiar with the climate there, but in parts with cold winters you are more likely to encounter dry air issues during the cold months.
One thing that could be happening is that the glue on the underside of the wood is acting as a seal on just that side, inhibiting the wood from 'breathing' underneath. The only surface area for moisture to leave the wood is on top. A solution that allows the wood to better breath on the bottom, or simply avoids using glue or too much glue, might help. But then you need make sure the vapor barrier is doing its job or you will end up back where you started with too much moisture underneath, the expert seems to imply you no longer have that issue though.
You can still end up with this problem with engineered floors. It could still be a problem with an unknown source of moisture throwing things out of balance as well. I'd see what the neighbors are doing as a solution for your area and if they have similar problems before I spend more money.
Best Answer
Water based glue quickly drys out and has been used for centuries. If it created rot we would have no antiques as most very old joinery is held together by tight joints and glue only. Two much glue wipe the excess but it will dry if their is an internal puddle and won’t cause rot.