Submillimetre galaxies represent a rapid growth phase of both star formation and massive galaxies. Mapping SMGs in galaxy protoclusters provides key insights into where and how these extreme starbursts take place in connections with the assembly of the large-scale structure in the early Universe. We search for SMGs at 850 $\rm{\mu m}$ using JCMT/SCUBA-2 in two massive protoclusters at z = 2.24, BOSS1244 and BOSS1542, and detect 43 and 54 sources with S850 > 4 mJy at the 4σ level within an effective area of 264 arcmin2, respectively. We construct the intrinsic number counts and find that the abundance of SMGs is 2.0 ± 0.3 and 2.1 ± 0.2 times that of the general fields, confirming that BOSS1244 and BOSS1542 contain a higher fraction of dusty galaxies with strongly enhanced star formation. The volume densities of the SMGs are estimated to be ~15-30 times the average, significantly higher than the overdensity factor (~6) traced by H α emission-line galaxies (HAEs). More importantly, we discover a prominent offset between the spatial distributions of the two populations in these two protoclusters - SMGs are mostly located around the high-density regions of HAEs, and few are seen inside these regions. This finding may have revealed for the first time the occurrence of violent star formation enhancement in the outskirts of the HAE density peaks, likely driven by the boosting of gas supplies and/or starburst triggering events. Meanwhile, the lack of SMGs inside the most overdense regions at z ~ 2 implies a transition to the environment disfavouring extreme starbursts.