Should I update Java on my Mac?

If there were any doubt about a good source of such an update

this is fairly recent link to get 'older Java version' for later macOS.

You may need this older version to facilitate a later one.

• Download Java for OS X 2017-001:
https://support.apple.com/kb/DL1572?locale=en_US

"..Java for macOS 2017-001 installs the legacy Java 6 runtime for macOS
10.13 High Sierra, macOS 10.12 Sierra, macOS 10.11 El Capitan, macOS
10.10 Yosemite, macOS 10.9 Mavericks, macOS 10.8 Mountain Lion, and
macOS 10.7 Lion.."

..There may be newer, but if your popup was due to adware, watch out..

See this article Get Java for your Mac - Apple Support

However another article macOS Sierra: Protect your Mac from malware

In addition to apps, other types of files may not be safe. Scripts, web archives, and Java archives have the potential to cause harm to your system. Of course, not all files like this are unsafe, but you should exercise caution when opening any such downloaded file. An alert appears when you first try to open these files.

Yes.