SSDP is multicast, being sent to address 188.8.131.52.
Multicast does not cross any subnet border without help from a router. If the given Wifi SSID is bridged into a wired network (or a VLAN thereof), these multicasts will reach the wired part of the (V)LAN.
A router must be explicitely enabled to forward multicast - but that's a huge topic in itself beyond this question.
On a sideline:
The related protocol suite from zeroconf networking (a.k.a. Rendevous/Bonjour, Avahi) also uses multicast, but in a fashion which makes it ineffective to route. They set TTL 255 in the packet's IP header, which a router decrements to 254, but zeroconf libraries on the end systems refuse to accept these packets if TTL is not 255. Some routers and L3 switches support a proxy feature for zeroconf, acting as application layer relay/forwarder for zeroconf between subnets.
SSDP seems to be using TTL=4 in the IP header (although the Internet finds SSDP sample captures with TTL=1); so if you enabled routers to forward multicast between subnets, SSDP messages might be able cross 3 routing hops.