I was able to get the client running on my Pi2b by running the following:
systemctl stop pulseway
wget http://ftp.debian.org/debian/pool/main/o/openssl/libssl1.0.0_1.0.1t-1+deb8u8_armhf.deb
dpkg -i libssl1.0.0_1.0.1t-1+deb8u8_armhf.deb ldconfig
systemctl start pulseway
systemctl status pulseway
● pulseway.service - LSB: Monitor and Control Everything IT from Any Smartphone or Tablet
Loaded: loaded (/etc/init.d/pulseway; generated; vendor preset: enabled)
Active: active (running) since Sun 2018-07-15 02:16:42 AEST; 11s ago
Docs: man:systemd-sysv-generator(8)
Process: 18044 ExecStop=/etc/init.d/pulseway stop (code=exited, status=0/SUCCESS)
Process: 18078 ExecStart=/etc/init.d/pulseway start (code=exited, status=0/SUCCESS)
CGroup: /system.slice/pulseway.service
├─18085 /usr/sbin/pulsewayd
├─18106 sh -c awk -v a="$(awk '/cpu /{print $2+$4,$2+$4+$5}' /proc/stat; sleep 1)" '/cpu /{split(a,b," "); print 100*($2+$4-b[1])/($2+$4+$5-b[2])}' /proc/stat 2>&1
└─18107 sleep 1
Jul 15 02:16:42 prkpi2b systemd[1]: Starting LSB: Monitor and Control Everything IT from Any Smartphone or Tablet...
Jul 15 02:16:42 prkpi2b systemd[1]: Started LSB: Monitor and Control Everything IT from Any Smartphone or Tablet.
Jul 15 02:16:42 prkpi2b pulseway[18085]: Configuration read successfully!
# uname -a
Linux prkpi2b 4.14.34-v7+ #1110 SMP Mon Apr 16 15:18:51 BST 2018 armv7l GNU/Linux
# dpkg -l |grep libssl
ii libssl1.0.0:armhf 1.0.1t-1+deb8u8 armhf Secure Sockets Layer toolkit - shared libraries
ii libssl1.0.2:armhf 1.0.2l-2+deb9u3 armhf Secure Sockets Layer toolkit - shared libraries
ii libssl1.1:armhf 1.1.0f-3+deb9u2 armhf Secure Sockets Layer toolkit - shared libraries
# grep -i pulseway /var/log/syslog
Jul 15 02:08:20 localhost pulseway[17976]: /usr/sbin/pulsewayd: /usr/lib/arm-linux-gnueabihf/libcrypto.so.1.0.0: version `OPENSSL_1.0.0' not found (required by /usr/sbin/pulsewayd)
Jul 15 02:08:20 localhost pulseway[17976]: /usr/sbin/pulsewayd: /usr/lib/arm-linux-gnueabihf/libssl.so.1.0.0: version `OPENSSL_1.0.0' not found (required by /usr/sbin/pulsewayd)
Jul 15 02:12:31 localhost pulseway[18023]: /usr/sbin/pulsewayd: /usr/lib/arm-linux-gnueabihf/libcrypto.so.1.0.0: version `OPENSSL_1.0.0' not found (required by /usr/sbin/pulsewayd)
Jul 15 02:12:31 localhost pulseway[18023]: /usr/sbin/pulsewayd: /usr/lib/arm-linux-gnueabihf/libssl.so.1.0.0: version `OPENSSL_1.0.0' not found (required by /usr/sbin/pulsewayd)
Jul 15 02:16:42 localhost pulseway: Starting Pulseway Daemon version 5.4 (2018021301)
Jul 15 02:16:42 localhost pulseway: Configuration read successfully!
Then checked the console and could see my Pi in there. Note the "ldconfig" command on the 4th line in bold - that updates the LD cache (linked libraries) which I'm guessing is why you were still getting the errors even though you had installed the v1.0.0 package.
