procedure TProcessListenerController.AddListener(ANode: string; AAutoStart: Boolean = True; AAutoStop: Boolean = False);
begin
  ....
  ANodeListener := TNodeListener.Create(Self, ANode, FOnLog);  
  if AAutoStart then begin
    ANodeListener.Run(AAutoStop); //здесь TTask.Create, затем старт
  end;
end;

.........

for I := Low(AHosts) to High(AHosts) do begin
    FController.AddListener(AHosts[I], False);
end;

12.02.2020 16:09:51.489 ~dbg~ Created
12.02.2020 16:09:51.490 ~dbg~ TryConnect
12.02.2020 16:10:14.755 ~dbg~ connection timeout

12.02.2020 16:10:12.572 ~dbg~ Created
12.02.2020 16:10:12.572 ~dbg~ TryConnect

function TDBXConnectionFactory.GetConnection(const DBXContext: TDBXContext;
  const ConnectionProperties: TDBXProperties): TDBXConnection;
var
  ConnectionBuilder:  TDBXConnectionBuilder;
  DelegatePath:       TDBXDelegateItem;
  CombinedProperties: TDBXProperties;
begin
  CombinedProperties := CombineDriverProperties(ConnectionProperties);
  DelegatePath := CreateDelegatePath('', CombinedProperties);
  ConnectionBuilder := TDBXConnectionBuilder.Create;
  try
    ConnectionBuilder.FDelegatePath               := DelegatePath;
    ConnectionBuilder.FConnectionFactory          := Self;
    ConnectionBuilder.FDBXContext                 := TDBXContext.Create(DBXContext);
    ConnectionBuilder.FInputConnectionName        := CombinedProperties[TDBXPropertyNames.ConnectionName];
    ConnectionBuilder.FInputConnectionProperties  := ConnectionProperties;
    ConnectionBuilder.FInputUserName              := CombinedProperties[TDBXPropertyNames.UserName];
    ConnectionBuilder.FInputPassword              := CombinedProperties[TDBXPropertyNames.Password];
    Result := ConnectionBuilder.CreateConnection;
    try
      Result.Open;
    except
      Result.Free;
      raise;
    end;
  finally
    ConnectionBuilder.Free;
  end;
end;

    ConnectionFactory.Lock;
    try
      FDBXConnection := ConnectionFactory.GetConnection(ConnectionProps);
    finally
      ConnectionFactory.Unlock;
    end;