You can get iterm2 to open up tabs, new splits and even new windows in the current working directory. This will show you how to set this up for new splits
1) Open up Settings and click profiles tab
2) Select default profile in list
3) Making sure general General subtab is open, in the working directory section select advanced configuration
4) click edit
5) In new dialog in the Working directory for new split panes section, select "Reuse previous session's directory"
6) Click ok
7) Restart iterm2