Why does atheroma contain thromplastin/tissue factor?
Tissue factor is present in subendothelial tissue and leukocytes - in this case this would be within the atheroma since the atheroma consists of damaged endothelium.

Tissue factor's presence in the subendotheilum in general implies that whenever the endothelium is damaged, tissue factor is released which promotes clotting at that site. Clotting starts after an atheroma ruptures because up until that point all the tissue factor is encased within the atheroma, protected from direct contact with the bloodstream - there is still no superficial injury to the endothelium to expose the underlying tissue factor that would signal the clotting cascade to begin. Therefore, clotting only starts after the atheroma ruptures and all the tissue factor stored within the atheroma is released into the blood vessel. 

It is worth noting here that in homeostasis without any injury, the coagulation cascade and fibrinolytic pathways (the clot-lysis or pathways) are both active, but they balance out each other's effects. Disruption of this balance due to pathology, injury, or other insult causes an imbalance between the two pathways which the body seeks to rectify. The imbalance is what leads to clot lysis (in the case of wound healing - after the wound has healed) and clot formation (in the case of a new injury). 

Sources:   


https://www.ahajournals.org/doi/full/10.1161/01.CIR.94.6.1226
https://www.ahajournals.org/doi/full/10.1161/01.CIR.96.2.396
https://ascpt.onlinelibrary.wiley.com/doi/pdf/10.1111/j.1752-8062.2011.00351.x