The viruses that cause fig mottling disease (FMD) are normally isolated from leaf tissue. Viral RNA from the more prevalent viruses, like FMV, has been detected in other fig tissues including roots. In an infected tree, the assumption is the virus is in all its cells.
As reported by Flock and Wallace in 1957, eriophyid mites can transfer mosaic disease in less than 10 days.
http://californiaagriculture.ucanr.org/landingpage.cfm?articleid=ca.v011n01p12
Mites are impossible to see, for me anyway, without magnification. So, they are easy to miss. It is possible that you have fig mites in your growing area and the mosaic disease was transferred from one or more of your infected plants. If a tree is infected with any FMD causing virus, elimination mites, assuming they are present, will NOT eliminate the virus(es) from that tree. Eliminating mites should prevent spread of virus variants within your collection of trees.
Because FMV is an RNA virus and RNA viruses normally have error-prone polymerases, there are lots of minor variants of FMV. A publication published in 2016 showed as much as 16% RNA sequence variation across 34 FMV isolates in genetic sequence databases. It is not known how each variant might impact mottling disease. Just to make things yet more complex, at least 9 additional fig viruses that cause mottling have been identified in the past few years causing the disease to be referred to by the scientists as fig mosaic (or mottling) disease, FMD for short. They are:
Fig Leaf Mottle-Associated Virsus 1 & 2 (FLMaV 1 & 2)
Fig Mild Mottle-Associated Virus (FMMaV)
Fig Latent Virus 1 (FLV-1)
Arkansas Fig Closterovirus 1 & 2 (AFCV 1 & 2)
Fig Badnavirus-1 (FBaV 1)
Fig Cryptic Virus (FCV)
Fig Fleck Associated Virus (FFkaV)
Several of the above viruses are also RNA viruses with meaningful variation between different isolates just to make the puzzle more annoying. Most of these viruses can apparently be clear an infected tree with scientific methods (heat therapy and/or meristem tip culture in vitro). One of the viruses is a retrovirus that has inserted its genome into the plant's DNA and can not be cured by any method if present.
The Falk lab at UC Davis and the Martelli lab in Italy were the 2 groups to isolate and get the genetic sequence of FMV.
http://apsjournals.apsnet.org/doi/pdf/10.1094/PDIS-93-1-0004
http://vir.sgmjournals.org/content/90/5/1281.full.pdf+html
It appears that FMV is not transmitted in seedlings. However, FLV-1 is reported to be transmitted in seedlings. I do not know about the other viruses.
http://sipav.org/main/jpp/index.php/jpp/article/view/563
Reports are starting to appear of efforts to screen trees across broad areas for FMV and other viruses. The ones that I have seen find FMV broadly distributed with a lot of variation in the distribution of the other fig viruses. They are using PCR based methods to detect. My guess is they are getting some false negatives even when >90% rates of infection are found.
I hope this is useful. Good luck with your figs!