  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$\,\mu m$ using JCMT/SCUBA-2 in two massive protoclusters at
$z=2.24$, BOSS1244 and BOSS1542, and detect 43 and 54 sources with
$S_{850}>4\,$mJy at the $4\sigma$ level within an effective area of
264$\,$arcmin$^2$, respectively. We construct the intrinsic number counts and
find that the abundance of SMGs is $2.0\pm0.3$ and $2.1\pm0.2$ 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 $\sim15-$30 times the average,
significantly higher than the overdensity factor ($\sim 6$) traced by H$\alpha$
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 $z\sim2$ implies a transition to the environment
disfavouring extreme starbursts.
