I did this

1. Edit /etc/resolve.conf to use a bad DNS server.
2. time curl https://github.com/ --max-time 1 -v
   And curl exits after 5 seconds. The output is

time curl https://github.com/ --max-time 1 -v
* Resolving timed out after 1000 milliseconds
* Could not resolve host: github.com
* stopped the pause stream!
* Closing connection 0
curl: (28) Resolving timed out after 1000 milliseconds
curl https://github.com/ --max-time 1 -v  0.02s user 0.02s system 0% cpu 5.042 total

I expected the following

curl exits after 1 second.
Document at https://ec.haxx.se/usingcurl-timeouts.html says "When the set time has elapsed, curl will exit no matter what is going on at that moment", so I think this is a bug.

curl/libcurl version

curl 7.61.0 (x86_64-pc-linux-gnu) libcurl/7.61.0 OpenSSL/1.1.0i zlib/1.2.11 libidn2/2.0.5 libpsl/0.20.2 (+libidn2/2.0.4) nghttp2/1.32.0
Release-Date: 2018-07-11
Protocols: dict file ftp ftps gopher http https imap imaps pop3 pop3s rtsp smb smbs smtp smtps telnet tftp
Features: AsynchDNS IDN IPv6 Largefile GSS-API Kerberos SPNEGO NTLM NTLM_WB SSL libz TLS-SRP HTTP2 UnixSockets HTTPS-proxy PSL

operating system

Arch Linux