It sounds like you don't really need to work out likely expansion and contraction of the wood in your table because you've found a workable solution, i.e., a generous allowance around the tile or tiles, plus a flexible filler between wood and tile. And the wood you're using is relatively small in section anyway, meaning expansion and contraction is likely to be of relatively little importance, although that's not always the case because sometimes even small dimensional change in small sections of wood can matter - it depends on the structure and its use.
But, yes, if you really wanted to, or need to, you can come up with calculations for likely expansion and contraction of wood across the grain. As others have said, atmospheric relative humidity (RH) is the primary contributory factor, although temperature has a relatively small role to play.
Basically, if you know the typical seasonal range of the RH affecting the wood, whether it's used outside or inside, and you know the percentage movement factor for the species of wood you're dealing with, you can do some sums to calculate the likely maximum and minimum size of the wood across the grain over the course of a year, and use this to make necessary design and technical choices.
So, for example, if you have a tangentially sawn European oak panel 950 mm wide that's at ~7% moisture content (MC) because it's acclimatised at the driest time of year to an atmospheric RH of ~40% at an average of ~20º C, and later in the year as the RH rises to it's highest level to an average of 65% RH at a similar average 20º C+ the wood will gradually move towards about 12.5% MC. Knowing this information allows you do sums and calculate that your 950 mm wide panel is likely to expand in width by approximately 5 - 6 mm to roughly 955 - 956 mm. Then, as the seasonal average RH moves back towards about 40% RH, the panel will reduce in width towards its original 950 mm.
I'm aware of what I think is a pretty good source of information on this subject of water, water vapour, temperature, and wood, but I'd probably contravene forum rules if I pointed you towards it, so I won't, ha, ha. Slainte.