I generate correct deployment config by script, but deployment throws ssh error

Checked that and it worked fine for me. Did you paste the files into .idea folder while the project was closed?

Could you please check if you have correct Deployment Mappings on Mappings tab after your project creation? I've recently faced a similar problem and perhaps they have something common: https://youtrack.jetbrains.com/issue/WI-68662

mapping is ok.

> Checked that and it worked fine for me. 
did you tried to generate config, which is different from the current?

If I generate the same config as current, everything works fine, but I need to generate different)

> Did you paste the files into .idea folder while the project was closed?
I generate configs and paste them into .idea folder while WS is opened. I don't close it. I just push 'Reload from disk' on .idea folder, to make WS see configs and start pushing "test connection" button procedure)

> did you tried to generate config, which is different from the current?

I've created a deployment configuration that wasn't existing before in a project. Do you mean that?

my templates are:

deploymen.xml

<?xml version="1.0" encoding="UTF-8"?>
<project version="4">
  <component name="PublishConfigData" serverName="nanny" remoteFilesAllowedToDisappearOnAutoupload="false" confirmBeforeUploading="false">
    <option name="confirmBeforeUploading" value="false" />
    <serverData>
      <paths name="nanny">
        <serverdata>
          <mappings>
            <mapping deploy="/" local="$PROJECT_DIR$" web="/" />
          </mappings>
        </serverdata>
      </paths>
    </serverData>
  </component>
</project>

sshConfigs.xml

<?xml version="1.0" encoding="UTF-8"?>
<project version="4">
  <component name="SshConfigs">
    <configs>
      <sshConfig authType="OPEN_SSH" host="{{ env.host }}" id="{{ env.ssh_conf_id }}" port="22" nameFormat="DESCRIPTIVE" username="{{ env.username }} " useOpenSSHConfig="true" />
    </configs>
  </component>
</project>

webServers.xml

<?xml version="1.0" encoding="UTF-8"?>
<project version="4">
  <component name="WebServers">
    <option name="servers">
      <webServer id="{{ env.web_server_id }}" name="nanny" url="http://localhost">
        <fileTransfer rootFolder="{{ env.root_folder }}" accessType="SFTP" host="{{ env.host }}" port="22" sshConfigId="{{ env.ssh_conf_id }}" sshConfig="{{ env.username }}@{{ env.host }}:22 agent" authAgent="true">
          <advancedOptions>
            <advancedOptions dataProtectionLevel="Private" keepAliveTimeout="0" passiveMode="true" shareSSLContext="true" isUseRsync="true" />
          </advancedOptions>
        </fileTransfer>
      </webServer>
    </option>
  </component>
</project>

and templater.bash

#!/usr/bin/env bash

ssh_command=$1;

export host=$4;

export username=$3;

echo "username $username"

export root_folder=$(eval "${1} ${2} '${3}' ${4}  -o StrictHostKeyChecking=no 'pwd'");

export ssh_conf_id='693ca004-3fc9-4ca4-a927-f8f0367cb5eb';

export web_server_id='4c04b2af-fa14-4fdd-b483-4efad8f84ba9';

templater -d .idea

ssh_conf_id and web_server_id were taken from configs generated by WS

May be you see something wrong here?)

Why it starts working after "test connection" buttons?)

Looks fine to me. Unfortunately I can't see why it works only after pressing "test connection". Perhaps there are some internal mechanisms, similar to caching, that aren't populated till you press that button. 

I have a question that is kind of a follow-up question to this one. I do as the OP says, with the difference that I generate all UUIDs (SSH Config ID, Web Server ID etc.) by msyelf. The script works, but the mapping and path exclusions provided exaclty as explained in the OP's templates do not show up in the UI..?