If your interface is configured as layer 3, your device will not maintain a list of MAC addresses outside of your subnet and you will not populate an ethernet table, even if one exists. The only reason your router cares about MAC addresses in a layer 3 context is so it knows where to send either routed (to next-hop) or same-subnet packets to. These are stored in the ARP table. If there is a ip mismatch between you and your carrier then their IP and MAC will not show up in your ARP table.
Therefore: If you want to analyze traffic that you are receiving from your carrier in an effort to troubleshoot then you should either:
1. Mirror that port and capture traffic with wireshark, or
2. Configure interface-level packet-capturing (https://www.juniper.net/documentation/en_US/junos/topics/concept/security-packet-capture-overview.html) and look at the capture offline
3. As you mentioned, configure your interface as layer 2 to see if your carrier's MAC address shows up. This requires that your device supports ethernet switching and that they are actively sending traffic.
Your Cisco router will also not have a mac table unless it has a switching module. Perhaps you are thinking of a layer 3 switch. It's certainly possible that Cisco will helpfully add ARP entries to the MAC table but Juniper does not do this.
Router>show hardware
Cisco IOS Software, C1900 Software (C1900-UNIVERSALK9-M), Version 15.0(1)M6, RELEASE SOFTWARE (fc1)
Router#sho interfaces gi0/0
GigabitEthernet0/0 is down, line protocol is up
Hardware is CN Gigabit Ethernet, address is 0007.1124.f200 (bia 0007.1124.f200)
Internet address is 192.168.0.1/24
Router>show ?
...
login Display Secure Login Configurations and State
management Display the management applications
mdf Show the names of configured EMM menus
memory Memory statistics
microcode show configured microcode for downloadable hardware
modemcap Show Modem Capabilities database
monitor Monitoring different system events
mtm MTM
network-clocks Network clocks information
...
Router>show